V. Lakshmikantham

The aim of the paper is to give a theorem about the existence and uniqueness of a solution of a nonlocal Cauchy problem for an ordinary differential equation in a … The aim of the paper is to give a theorem about the existence and uniqueness of a solution of a nonlocal Cauchy problem for an ordinary differential equation in a Banach space. The Banach theorem about the fixed point is used to prove the existence and uniqueness of a solution of the problem considered. The result obtained in this paper can be applied among other things to the description of motion phenomena with better effect than the classical Cauchy problem.

Theory of Fuzzy Differential Equations and Inclusions

2004-11-23

V. Lakshmikantham , R. N. Mohapatra

Fuzzy differential functions are applicable to real-world problems in engineering, computer science, and social science. That relevance makes for rapid development of new ideas and theories. This volume is a … Fuzzy differential functions are applicable to real-world problems in engineering, computer science, and social science. That relevance makes for rapid development of new ideas and theories. This volume is a timely introduction to the subject that describes the current state of the theory of fuzzy differential equations and inclusions and provides a systematic account of recent developments. The chapters are presented in a clear and logical way and include the preliminary material for fuzzy set theory; a description of calculus for fuzzy functions, an investigation of the basic theory of fuzzy differential equations, and an introduction to fuzzy differential inclusions.

Theory Of Difference Equations Numerical Methods And Applications

2002-06-12

V. Lakshmikantham , V. Trigiante

Provides a clear and comprehensive overview of the fundamental theories, numerical methods, and iterative processes encountered in difference calculus. Explores classical problems such as orthological polynomials, the Euclidean algorithm, roots … Provides a clear and comprehensive overview of the fundamental theories, numerical methods, and iterative processes encountered in difference calculus. Explores classical problems such as orthological polynomials, the Euclidean algorithm, roots of polynomials, and well-conditioning.

Dynamic Systems on Measure Chains

1996-01-01

V. Lakshmikantham , S. Sivasundaram , Bıllûr Kaymakçalan

An Introduction to Nonlinear Boundary Value Problems

1974-01-01

Stephen R. Bernfeld , V. Lakshmikantham

Monotone Iterative Techniques for Discontinuous Nonlinear Differential Equations

2017-09-29

Seppo Heikkilä , V. Lakshmikantham

""Providing the theoretical framework to model phenomena with discontinuous changes, this unique reference presents a generalized monotone iterative method in terms of upper and lower solutions appropriate for the study … ""Providing the theoretical framework to model phenomena with discontinuous changes, this unique reference presents a generalized monotone iterative method in terms of upper and lower solutions appropriate for the study of discontinuous nonlinear differential equations and applies this method to derive suitable fixed point theorems in ordered abstract spaces.

Differential Equations in Abstract Spaces

1972-01-01

G. Ladas , V. Lakshmikantham

General uniqueness and monotone iterative technique for fractional differential equations

2008-01-09

V. Lakshmikantham , A. S. Vatsala

Uniqueness and Nonuniqueness Criteria for Ordinary Differential Equations

1993-03-01

Ravi P. Agarwal , V. Lakshmikantham

First order differential equations first order differential systems higher order differential equations differential equations in abstract spaces complex differential equations functional differential equations impulsive differential equations differential equations with hysteresis … First order differential equations first order differential systems higher order differential equations differential equations in abstract spaces complex differential equations functional differential equations impulsive differential equations differential equations with hysteresis generalized differential equations.

Generalized Quasilinearization for Nonlinear Problems

1998-01-01

V. Lakshmikantham , A. S. Vatsala

Stability of conditionally invariant sets and controlleduncertain dynamic systems on time scales

1995-01-01

V. Lakshmikantham , Z. Drici

A basic feedback control problem is that of obtaining some desired stability property from a system which contains uncertainties due to unknown inputs into the system. Despite such imperfect knowledge … A basic feedback control problem is that of obtaining some desired stability property from a system which contains uncertainties due to unknown inputs into the system. Despite such imperfect knowledge in the selected mathematical model, we often seek to devise controllers that will steer the system in a certain required fashion. Various classes of controllers whose design is based on the method of Lyapunov are known for both discrete [4], [10], [15], and continuous [3–9], [11] models described by difference and differential equations, respectively. Recently, a theory for what is known as dynamic systems on time scales has been built which incorporates both continuous and discrete times, namely, time as an arbitrary closed sets of reals, and allows us to handle both systems simultaneously [1], [2], [12], [13]. This theory permits one to get some insight into and better understanding of the subtle differences between discrete and continuous systems. We shall, in this paper, utilize the framework of the theory of dynamic systems on time scales to investigate the stability properties of conditionally invariant sets which are then applied to discuss controlled systems with uncertain elements. For the notion of conditionally invariant set and its stability properties, see [14]. Our results offer a new approach to the problem in question.

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Basic results on hybrid differential equations

2009-11-01

Bapurao C. Dhage , V. Lakshmikantham

THEORY OF FRACTIONAL DIFFERENTIAL INEQUALITIES AND APPLICATIONS

2007-01-01

V. Lakshmikantham , A. S. Vatsala

In this paper, we develop the theory of fractional dieren tial inequalities involving Riemann-Loiuville dieren tial operators of order 0 < q < 1, use it for the existence of … In this paper, we develop the theory of fractional dieren tial inequalities involving Riemann-Loiuville dieren tial operators of order 0 < q < 1, use it for the existence of extremal solutions and global existence. Necessary tools are discussed and the comparison principle is proved which will be useful for further study of qualitative behavior of solutions.

Nonlinear Analysis: Theory, Methods and Applications

1978-04-01

A. M. Hey , V. Lakshmikantham

Theory of Differential Equations with Unbounded Delay

1994-01-01

V. Lakshmikantham , Lizhi Wen , Binggen Zhang

Sharp conditions for oscillations caused by delays

1979-08-01

G. Ladas , V. Lakshmikantham

AMS (MOS) subject classification (1970): Primary 34K15; Secondary 34K25, 34E10. A sufficient condition under which all solutions of the delay differential equation , where p(t≤0 and continuous and τ>0 and … AMS (MOS) subject classification (1970): Primary 34K15; Secondary 34K25, 34E10. A sufficient condition under which all solutions of the delay differential equation , where p(t≤0 and continuous and τ>0 and constant, are oscillatory is presented. It is explained that the condition is the best possible for oscillations. When the coefficient p(t) in equation (1) is a positive constant, p, then the condition becomes pτe>0 which is necessary and sufficient for all solutions of the DDE to be oscillatory.

Theory of Fractional Differential Equations in a Banach Space

2007-09-12

V. Lakshmikantham , J. Vasundhara Devi

In this paper, the basic theory of fractional differential equations in a Banach Space is discussed including flow invariance and theory of inequalities in cones. In this paper, the basic theory of fractional differential equations in a Banach Space is discussed including flow invariance and theory of inequalities in cones.

Nonlinear Equations in Abstract Spaces

1978-01-01

V. Lakshmikantham

OSCILLATIONS OF HIGHER-ORDER RETARDED DIFFERENTIAL EQUATIONS GENERATED BY THE RETARDED ARGUMENT

1972-01-01

G. Ladas , V. Lakshmikantham , John S. Papadakis

Nagumo-type uniqueness result for fractional differential equations

2009-01-30

V. Lakshmikantham , S. Leela

Initial and boundary value problems for fuzzy differential equations

2003-05-19

Donal O’Regan , V. Lakshmikantham , Juan J. Nieto

An extension of the method of quasilinearization

1994-08-01

V. Lakshmikantham

Existence and monotone method for periodic solutions of first-order differential equations

1983-01-01

V. Lakshmikantham , S. Leela

Revisiting fuzzy differential equations

2004-07-10

T. Gnana Bhaskar , V. Lakshmikantham , J. Vasundhara Devi

On quasi stability for impulsive differential systems

1989-07-01

V. Lakshmikantham , Xinzhi Liu

Monotone iterative technique for differential equations in a Banach space

1982-06-01

Sen-Wo Du , V. Lakshmikantham

Existence and interrelation between set and fuzzy differential equations

2003-08-08

V. Lakshmikantham , А. А. Толстоногов

Book Review: Introduction to spectral theory: Selfadjoint ordinary differential operators

1977-03-01

V. Lakshmikantham

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Trends in Theory and Practice of Nonlinear Differential Equations.

1984-10-01

W. G. , V. Lakshmikantham

Comparison principle for impulsive differential equations with variable times and stability theory

1994-02-01

V. Lakshmikantham , S. Leela , Saroop K. Kaul

A Krasnoselskii–Krein-type uniqueness result for fractional differential equations

2009-02-11

V. Lakshmikantham , S. Leela

Extremal solutions, comparison principle and stability criteria for impulsive differential equations with variable times

1994-05-01

Saroop K. Kaul , V. Lakshmikantham , S. Leela

Coupled Random Fixed Point Theorems for Nonlinear Contractions in Partially Ordered Metric Spaces

2009-10-21

Łjubomir Ćirić , V. Lakshmikantham

Abstract Abstract Let (X, ≤) be a partially ordered set and suppose there is a metric d on X such that (X, d) is a complete separable metric space and … Abstract Abstract Let (X, ≤) be a partially ordered set and suppose there is a metric d on X such that (X, d) is a complete separable metric space and (Ω, Σ) be a measurable space. In this article a pair of random mappings F: Ω × (X × X) → X and g: Ω × X → X, where F has a mixed g-monotone property on X, and F and g satisfy the non-linear contractive condition (5) below, are introduced and investigated. Two coupled random coincidence and coupled random fixed point theorems are proved. These results are random versions and extensions of recent results of Lakshmikantham and Ćirić [V. Lakshmikantham and Lj. Ćirić, Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces. Nonlinear Anal.—Theor. 70(12) (2009): 4341–4349] and include several recent developments. Keywords: Coupled coincidenceCoupled fixed pointMeasurable mappingMixed monotone mappingRandom operatorMathematics Subject Classification: Primary 47H10Secondary 54H25, 34B15

Stability criteria for impulsive differential equations in terms of two measures

1989-02-01

V. Lakshmikantham , Xinzhi Liu

Multiple solutions of two-point boundary value problems of ordinary differential equations in Banach spaces

1988-01-01

Dajun Guo , V. Lakshmikantham

On the existence of weak solutions of differential equations in nonreflexive banach spaces

1978-02-01

Evin Cramer , V. Lakshmikantham , A. R. Mitchell

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Remarks on first and second order periodic boundary value problems

1984-03-01

V. Lakshmikantham , S. Leela

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Periodic boundary value problems for second order impulsive differential systems

1989-01-01

Shouchuan Hu , V. Lakshmikantham

Further improvement of generalized quasilinearization method

1996-07-01

V. Lakshmikantham

On flow-invariant sets

1974-03-01

G.S. Ladde , V. Lakshmikantham

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Fixed point theorems of operators with ppf dependence in banach spaces

1977-01-01

Stephen R. Bernfeld , V. Lakshmikantham , Y.Madana Mohana Reddy

In this paper the theory of fixed point theorems of nonlinear whose domain and range are different Banach spaces are considered. Also the analogues of the Contraction Mapping Principle. Krasnoselskii's … In this paper the theory of fixed point theorems of nonlinear whose domain and range are different Banach spaces are considered. Also the analogues of the Contraction Mapping Principle. Krasnoselskii's fixed point theorem and a result on the convergence of quasinonexpansive mappings are dealt with. As an application, the existence and uniqueness of solutions of differential equations with retarded argument in Banach spaces are discussed

Comparison Principle for Impulsive Differential Equations with Variable Times

2020-12-12

V. Lakshmikantham

In this paper, we discuss the existence of extremal solutions for impulsive differential equations (IDE) with variable times using a new approach, develop the necessary comparison result parallel to the … In this paper, we discuss the existence of extremal solutions for impulsive differential equations (IDE) with variable times using a new approach, develop the necessary comparison result parallel to the one in ODE and apply it for the investigation of stability criteria. In the context of stability investigation, it is natural to consider the existence of a solution that meets each given barrier (hypersurface) exactly once i.e., the lack of pulse phenomenon. With this motivation, we also consider a result on existence of solutions which meet the given hypersurfaces only once and this result is a refinement of the known result in [5]. We do hope that the new idea of this paper will be of value in the study of qualitative behavior of solutions of IDE with variable times whose progress so far has been slow.

Abstract Differential Equations

2019-09-10

V. Lakshmikantham , Sadashiv G. Deo

Differential Equations with Delay

2019-09-10

V. Lakshmikantham , Sadashiv G. Deo

Stochastic Differential Equations

2019-09-10

V. Lakshmikantham , Sadashiv G. Deo

Monotone Iterative Techniques for Discontinuous Nonlinear Differential Equations

2017-09-29

Seppo Heikkilä , V. Lakshmikantham

Second Order Partial Differential Equations

2017-09-29

Seppo Heikkilä , V. Lakshmikantham

Differential Equations in Banach Spaces

2017-09-29

Seppo Heikkilä , V. Lakshmikantham

A UNIFIED MONOTONE ITERATIVE TECHNIQUE FOR NONLINEAR ELLIPTIC PROBLEMS VIA NONVARIATIONAL METHOD

2016-04-07

Semen Köksal , V. Lakshmikantham

A unified approach for the monotone iterative technique is discussed for the nonlinear elliptic boundary value problems when the nonlinear right-hand side is the sum of two monotone functions. This … A unified approach for the monotone iterative technique is discussed for the nonlinear elliptic boundary value problems when the nonlinear right-hand side is the sum of two monotone functions. This setting includes several results and can be applied to other nonlinear problems.

Variation of Parameters and Monotone Technique

2015-01-01

V. Lakshmikantham , S. Leela , Anatoly A. Martynyuk

In this chapter we stress the importance of nonlinear variation of parameters formulae for a variety of nonlinear problems as well as monotone iterative technique that offers constructive methods for … In this chapter we stress the importance of nonlinear variation of parameters formulae for a variety of nonlinear problems as well as monotone iterative technique that offers constructive methods for the existence of solution in a sector.

Stability of Perturbed Motion

2015-01-01

V. Lakshmikantham , S. Leela , Anatoly A. Martynyuk

In this chapter, stability considerations are extended to a variety of nonlinear systems utilizing the same versatile tools, namely, Lyapunov-like functions, theory of appropriate inequalities and different measures, that were … In this chapter, stability considerations are extended to a variety of nonlinear systems utilizing the same versatile tools, namely, Lyapunov-like functions, theory of appropriate inequalities and different measures, that were developed in the previous chapters. In order to avoid monotony, we have restricted ourselves to present only typical extensions which demonstrate the essential unity achieved and pave the way for further work.

Averaging Principle for Multifrequency Systems of Differential Equations

2010-02-16

A.A. Martynyuk , Eugeniu Grebenikov , V. Lakshmikantham +2 more

Asymptotic Methods in Resonance Analytical Dynamics presents new asymptotic methods for the analysis and construction of solutions (mainly periodic and quasiperiodic) of differential equations with small parameters. Along with some … Asymptotic Methods in Resonance Analytical Dynamics presents new asymptotic methods for the analysis and construction of solutions (mainly periodic and quasiperiodic) of differential equations with small parameters. Along with some background material and theory behind these methods, the authors also consider a variety of problems and applications in nonlinear mechanics and oscillation theory. The methods examined are based on two types: the generalized averaging technique of Krylov-Bogolubov and the numeric-analytical iterations of Lyapunov-Poincaré. This text provides a useful source of reference for postgraduates and researchers working in this area of applied mathematics.

Stability and asymptotic behaviour of solutions of differential equations in a Banach space

2010-01-01

V. Lakshmikantham

On the concept of solution for fractional differential equations with uncertainty

2009-11-18

Ravi P. Agarwal , V. Lakshmikantham , Juan J. Nieto

Basic results on hybrid differential equations

2009-11-01

Bapurao C. Dhage , V. Lakshmikantham

On global existence and attractivity results for nonlinear functional integral equations

2009-10-31

Bapurao C. Dhage , V. Lakshmikantham

Coupled Random Fixed Point Theorems for Nonlinear Contractions in Partially Ordered Metric Spaces

2009-10-21

Łjubomir Ćirić , V. Lakshmikantham

Fractional differential equations with a Krasnoselskii–Krein type condition

2009-07-15

T. Gnana Bhaskar , V. Lakshmikantham , S. Leela

A Krasnoselskii–Krein-type uniqueness result for fractional differential equations

2009-02-11

V. Lakshmikantham , S. Leela

Fixed point theorems in ordered Banach spaces via quasilinearization

2009-02-11

V. Lakshmikantham , Siegfried Carl , Seppo Heikkilä

WITHDRAWN: A fixed point theorem reflecting the ideas of Nagumo-type conditions

2009-02-01

V. Lakshmikantham , S. Leela

Nagumo-type uniqueness result for fractional differential equations

2009-01-30

V. Lakshmikantham , S. Leela

Miscellaneous Topics in Causal Systems

2009-01-01

V. Lakshmikantham , S. Leela , Z. Drici +1 more

This chapter deals with extensions and generalizations of causal differential equations to other important areas of nonlinear analysis. We begin with the set differential equations with causal operators naming them … This chapter deals with extensions and generalizations of causal differential equations to other important areas of nonlinear analysis. We begin with the set differential equations with causal operators naming them as causal set differential equations (CSDE). Set differential equations in a metric space has gained much attention recently due to its applicability to multivalued differential inclusions and fuzzy differential equations and its inclusion of ordinary differential systems as a special case. The generalization of this dynamic system to include causal differential equations would cover a wider variety of situations and therefore, it would initiate an interesting and useful branch of nonlinear analysis that requires further investigation.

WITHDRAWN: Stability theory for multi-order fractional differential equations

2008-11-01

V. Lakshmikantham , S. Leela

Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces

2008-10-18

V. Lakshmikantham , Łjubomir Ćirić

Nonsmooth analysis and fractional differential equations

2008-09-12

J. Vasundhara Devi , V. Lakshmikantham

Mean value theorem, Ultra Mittag-Leffler function and convergence of successive approximations for fractional differential equations

2008-08-01

M.P.K. Kishore , V. Lakshmikantham

In this paper an attempt is made to prove some mean value theorems for fractional differential equations. Further, a new function, called Ultra Mittag Leffler function is introduced which was … In this paper an attempt is made to prove some mean value theorems for fractional differential equations. Further, a new function, called Ultra Mittag Leffler function is introduced which was the outcome of proving existence and uniqueness result using successive approximations under Holder condition for fractional differential function.

General uniqueness and monotone iterative technique for fractional differential equations

2008-01-09

V. Lakshmikantham , A. S. Vatsala

Fractional Differential and Integral Equations of Riemann-Liouville versus Caputo

2008-01-01

A. S. Vatsala , V. Lakshmikantham , Michail D. Todorov

Recently fractional differential equations involving Riemann‐Loiuville type as well as Caputo type has gained importance due to its application. In this paper we compare and contrast these two types of … Recently fractional differential equations involving Riemann‐Loiuville type as well as Caputo type has gained importance due to its application. In this paper we compare and contrast these two types of equations and present the latest development relative to them.

Set Differential Equations in Fréchet Spaces

2008-01-01

George Galanis , T. Gnana Bhaskar , V. Lakshmikantham

It is known that a Fréchet space 𝔽 can be realized as a projective limit of a sequence of Banach spaces . The space Kc(𝔽) of all compact, convex subsets … It is known that a Fréchet space 𝔽 can be realized as a projective limit of a sequence of Banach spaces . The space Kc(𝔽) of all compact, convex subsets of a Fréchet space, 𝔽, is realized as a projective limit of the semilinear metric spaces . Using the notion of Hukuhara derivative for maps with values in Kc(𝔽), we prove the local and global existence theorems for an initial value problem associated with a set differential equation.

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Theory of fractional functional differential equations

2007-10-02

V. Lakshmikantham

Theory of Fractional Differential Equations in a Banach Space

2007-09-12

V. Lakshmikantham , J. Vasundhara Devi

Basic theory of fractional differential equations

2007-08-28

V. Lakshmikantham , A. S. Vatsala

Functional differential equations with Anticipation

2007-08-01

V. Lakshmikantham , J. Vasundhara Devi

An existence theorem for set differential inclusions in a semilinear metric space

2007-01-01

F. S. de Blasi , V. Lakshmikantham , T. Gnana Bhaskar

Using the notion of continuous approximate selec- tions, we establish an existence theorem for set differential inclusions in a semi-linear metric space. Using the notion of continuous approximate selec- tions, we establish an existence theorem for set differential inclusions in a semi-linear metric space.

PERSPECTIVES OF FUZZY INITIAL VALUE PROBLEMS

2007-01-01

Barnab As Bede , T. Gnana Bhaskar , V. Lakshmikantham

Recently it is proposed that the behavior of the solutions of fuzzy dieren tial equa- tions (FDEs) could be tamed by a suitable forcing term. In this context a case … Recently it is proposed that the behavior of the solutions of fuzzy dieren tial equa- tions (FDEs) could be tamed by a suitable forcing term. In this context a case has been made that FDEs need to be investigated as a separate discipline instead of treating them as fuzzy analogues of crisp counterparts. Here in this paper, we support this argument also by showing how dieren t formulations of a fuzzy dieren tial equation can lead to solutions with dieren t behaviors, adding richness to the theory of FDEs. For this aim we use the notions of Hukuhara dieren tial, generalized dieren tiability, dieren tial inclusions and the interpretation of FDEs by using Zadeh's extension principle on the classical solution. We also point out several possible research directions in the study of FDEs.

THEORY OF FRACTIONAL DIFFERENTIAL INEQUALITIES AND APPLICATIONS

2007-01-01

V. Lakshmikantham , A. S. Vatsala

Functional differential systems with retardation and anticipation

2006-06-13

T. Gnana Bhaskar , V. Lakshmikantham

Monotone iterative technique for functional differential equations with retardation and anticipation

2006-05-03

T. Gnana Bhaskar , V. Lakshmikantham , J. Vasundhara Devi

Fixed point theorems in partially ordered metric spaces and applications

2006-04-05

T. Gnana Bhaskar , V. Lakshmikantham

On initial-boundary value problems in bounded and unbounded domains for a class of nonlinear hyperbolic equations of the third order

2006-02-10

Tariel Kiguradze , V. Lakshmikantham

Stability in terms of two measures of hybrid systems with partially visible solutions

2005-05-11

V. Lakshmikantham , J. Vasundhara Devi , A. S. Vatsala

Nonlinear variation of parameters formula for set differential equations in a metric space

2005-04-04

T. Gnana Bhaskar , V. Lakshmikantham , J. Vasundhara Devi

Set valued functions in Fréchet spaces: Continuity, Hukuhara differentiability and applications to set differential equations

2005-02-17

George Galanis , T. Gnana Bhaskar , V. Lakshmikantham +1 more

Maximal Solutions and Existence Theory for Fuzzy Differential and Integral Equations

2005-01-01

Ravi P. Agarwal , Donal O’Regan , V. Lakshmikantham

New existence results are presented for fuzzy differential and integral equations. Our analysis combines the stacking theorem with results concerning the maximal solution for an appropriate differential equation. New existence results are presented for fuzzy differential and integral equations. Our analysis combines the stacking theorem with results concerning the maximal solution for an appropriate differential equation.

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Error: Precisely What, Why, and How

2005-01-01

V. Lakshmikantham , Sagar Sen

Error and Complexity in Numerical Methods

2005-01-01

V. Lakshmikantham , Sagar Sen

Nonresonant singular boundary value problems with sign changing nonlinearities

2004-12-15

Ravi P. Agarwal , Donal O’Regan , V. Lakshmikantham +1 more

Theory of Fuzzy Differential Equations and Inclusions

2004-11-23

V. Lakshmikantham , R. N. Mohapatra

Viability theory and fuzzy differential equations

2004-09-16

Ravi P. Agarwal , Donal O’Regan , V. Lakshmikantham

Generalized quasilinearization versus Newton’s method

2004-09-10

V. Lakshmikantham , A. S. Vatsala

Coauthor	Papers Together
S. Leela	43
A. S. Vatsala	23
Ravi P. Agarwal	15
Donal O’Regan	14
Stephen R. Bernfeld	13
Seppo Heikkilä	13
T. Gnana Bhaskar	13
G.S. Ladde	11
J. Vasundhara Devi	10
G. Ladas	9
Dajun Guo	9
Xinzhi Liu	9
S. Sivasundaram	8
Sagar Sen	7
Shouchuan Hu	6
Klaus Deimling	5
Juan J. Nieto	5
J. Eisenfeld	5
A. R. Mitchell	5
Binggen Zhang	5
Lizhi Wen	5
Semen Köksal	4
R. Kannan	4
Tariel Kiguradze	4
R. N. Mohapatra	4
Roger W. Mitchell	3
Jagdish Chandra	3
Sadashiv G. Deo	3
Saroop K. Kaul	3
Z. Drici	3
Naseer Shahzad	3
Siegfried Carl	3
Anatoly A. Martynyuk	2
Sudhakar G. Pandit	2
B.G. Zhang	2
K. N. Murty	2
B. B. Williams	2
Mohammad Khavanin	2
Nguyễn Văn Minh	2
Thomas G. Hallam	2
Łjubomir Ćirić	2
F.A. McRae	2
A. A. Gillespie	2
Murali Rao	2
П. П. Забрейко	2
Vinicio Moauro	2
Nikolaos S. Papageorgiou	2
Mansour Samimi	2
Bapurao C. Dhage	2
Y.Madana Mohana Reddy	2

Differential and Integral Inequalities

2019-01-01

Dorin Andrica , Themistocles M. Rassias

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An Introduction to Nonlinear Boundary Value Problems

1974-01-01

Stephen R. Bernfeld , V. Lakshmikantham

Differential and Integral Inequalities

1970-01-01

Wolfgang Walter

Theory of Fuzzy Differential Equations and Inclusions

2004-11-23

V. Lakshmikantham , R. N. Mohapatra

Differential and integral inequalities : theory and applications

1969-01-01

V. Lakshmikantham , S. Leela

Differential Equations in Abstract Spaces

1972-01-01

G. Ladas , V. Lakshmikantham

Fuzzy differential equations

1987-12-01

Osmo Kaleva

A monotone method for infinite systems of nonlinear boundary value problems

1978-06-01

Jagdish Chandra , V. Lakshmikantham , S. Leela

Elliptic boundary value problems suggested by nonlinear diffusion processes

1969-01-01

Herbert B. Keller

A monotone method for quasilinear boundary value problems

1974-09-01

Jagdish Chandra , Paul Wm. Davis

The cauchy problem for fuzzy differential equations

1990-05-01

Osmo Kaleva

Ordinary Differential Equations in Banach Spaces

1977-01-01

Klaus Deimling

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Existence and monotone method for periodic solutions of first-order differential equations

1983-01-01

V. Lakshmikantham , S. Leela

Minimal and maximal solutions of nonlinear boundary value problems

1977-07-01

Stephen R. Bernfeld , Jagdish Chandra

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Periodic solutions of nonlinear boundary value problems

1982-02-01

R. Kannan , V. Lakshmikantham

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Quasi-solutions and monotone method for systems of nonlinear boundary value problems

1981-01-01

V. Lakshmikantham , A. S. Vatsala

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Basic theory of fractional differential equations

2007-08-28

V. Lakshmikantham , A. S. Vatsala

Generalized Quasilinearization for Nonlinear Problems

1998-01-01

V. Lakshmikantham , A. S. Vatsala

Monotone Iterative Techniques for Discontinuous Nonlinear Differential Equations

2017-09-29

Seppo Heikkilä , V. Lakshmikantham

Quasi-solutions and their role in the qualitative theory of differential equations

1980-01-01

Klaus Deimling , V. Lakshmikantham

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Nonlinear Functional Analysis and its Applications

1990-01-01

Eberhard Zeidler

Regularity of solution sets for differential inclusions quasi-concave in a parameter

2000-01-01

P. H. Diamond , P. Watson

Maximum Principles in Differential Equations

1984-01-01

Murray H. Protter , Hans F. Weinberger

Differential equations on closed subsets of a Banach space

1973-01-01

R. H. Martin

In this paper the problem of existence of solutions to the initial value problem <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="u prime left-parenthesis t right-parenthesis equals upper A left-parenthesis t comma u … In this paper the problem of existence of solutions to the initial value problem <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="u prime left-parenthesis t right-parenthesis equals upper A left-parenthesis t comma u left-parenthesis t right-parenthesis right-parenthesis comma u left-parenthesis a right-parenthesis equals z"> <mml:semantics> <mml:mrow> <mml:msup> <mml:mi>u</mml:mi> <mml:mo>′</mml:mo> </mml:msup> <mml:mo stretchy="false">(</mml:mo> <mml:mi>t</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mo>=</mml:mo> <mml:mi>A</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>t</mml:mi> <mml:mo>,</mml:mo> <mml:mi>u</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>t</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mo stretchy="false">)</mml:mo> <mml:mo>,</mml:mo> <mml:mi>u</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>a</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mo>=</mml:mo> <mml:mi>z</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">u’(t) = A(t,u(t)),u(a) = z</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, is considered where <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper A colon left-bracket a comma b right-parenthesis times upper D right-arrow upper E"> <mml:semantics> <mml:mrow> <mml:mi>A</mml:mi> <mml:mo>:</mml:mo> <mml:mo stretchy="false">[</mml:mo> <mml:mi>a</mml:mi> <mml:mo>,</mml:mo> <mml:mi>b</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mo>×</mml:mo> <mml:mi>D</mml:mi> <mml:mo stretchy="false">→</mml:mo> <mml:mi>E</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">A:[a,b) \times D \to E</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is continuous, <italic>D</italic> is a closed subset of a Banach space <italic>E</italic>, and <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="z element-of upper D"> <mml:semantics> <mml:mrow> <mml:mi>z</mml:mi> <mml:mo>∈</mml:mo> <mml:mi>D</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">z \in D</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. With a dissipative type condition on <italic>A</italic>, we establish sufficient conditions for this initial value problem to have a solution. Using these results, we are able to characterize all continuous functions which are generators of nonlinear semigroups on <italic>D</italic>.

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Differential Inclusions in a Banach Space

2000-01-01

А. А. Толстоногов

Existence of periodic solutions of nonlinear boundary value problems and the method of upper and lower solutions

1984-01-01

R. Kannan , V. Akshmikantham

We study the existence of periodic solutions of second order nonlinear differential equations by combining the method of upper and lower solutions and the method of Alternative problems. The emphasis … We study the existence of periodic solutions of second order nonlinear differential equations by combining the method of upper and lower solutions and the method of Alternative problems. The emphasis in this paper is on the role of the boundary conditions in the definition of upper and lower solutions.

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On the Solution of Nonlinear Fractional-Order Differential Equations Used in the Modeling of Viscoplasticity

1999-01-01

Kai Diethelm , Alan D. Freed

Periodic boundary value problems for systems of second order differential equations

1973-01-01

J. Bebernes , Klaus Schmitt

Generalized quasilinearization for nonlinear problems

1999-02-01

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General uniqueness and monotone iterative technique for fractional differential equations

2008-01-09

V. Lakshmikantham , A. S. Vatsala

Relaxation in filled polymers: A fractional calculus approach

1995-10-22

Ralf Metzler , Winfried Schick , Hanns‐Georg Kilian +1 more

In recent years the fractional calculus approach to describing dynamic processes in disordered or complex systems such as relaxation or dielectric behavior in polymers or photo bleaching recovery in biologic … In recent years the fractional calculus approach to describing dynamic processes in disordered or complex systems such as relaxation or dielectric behavior in polymers or photo bleaching recovery in biologic membranes has proved to be an extraordinarily successful tool. In this paper we apply fractional relaxation to filled polymer networks and investigate the dependence of the decisive occurring parameters on the filler content. As a result, the dynamics of such complex systems may be well–described by our fractional model whereby the parameters agree with known phenomenological models.

Partial Differential Equations

1988-01-01

Shiing-Shen Chern

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Existence of solutions for ordinary differential equations in Banach spaces

1975-05-01

Tien-Yien Li

Remarks on Peano-like theorems for fuzzy differential equations

1991-11-01

Peter E. Kloeden

Perturbations of nonlinear systems of differential equations. II

1967-03-01

Fred Brauer

Lyapunov functions and autonomous differential equations in a Banach space

1973-03-01

R. H. Martin

A monotone method for a system of nonlinear parabolic differential equations

1981-01-01

Jagdish Chandra , F. G. Dressel , Paul Dennis Norman

Synopsis A monotone iteration scheme for the solution of the initial boundary problems associated with a system of semilinear parabolic differential equations has been developed that does not require the … Synopsis A monotone iteration scheme for the solution of the initial boundary problems associated with a system of semilinear parabolic differential equations has been developed that does not require the nonlinearities to be quasimonotone. The class of equations to which this scheme applies includes physical models that describe combustion processes involving Arrhenius reaction terms.

Basic properties of solutions of fuzzy differential equations

2001-02-01

V. Lakshmikantham , R. N. Mohapatra

Comparison principle and nonlinear contractions in abstract spaces

1975-02-01

J. Eisenfeld , V. Lakshmikantham

Analysis of Fractional Differential Equations

2002-01-01

Kai Diethelm , Neville J. Ford

Towards fuzzy differential calculus part 1: Integration of fuzzy mappings

1982-06-01

Didier Dubois , Henri Prade

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Towards fuzzy differential calculus part 3: Differentiation

1982-09-01

Didier Dubois , Henri Prade

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Functional Differential Equations

1971-01-01

Jack K. Hale

An extension of the method of quasilinearization

1994-08-01

V. Lakshmikantham

Optimal iterative schemes for computing the Moore-Penrose matrix inverse

1976-08-01

Sagar Sen , S. Prabhu

Among the iterative schemes for computing the Moore — Penrose inverse of a woll-conditioned matrix, only those which have an order of convergence three or two are computationally efficient. A … Among the iterative schemes for computing the Moore — Penrose inverse of a woll-conditioned matrix, only those which have an order of convergence three or two are computationally efficient. A Fortran programme for these schemes is provided.

Monotone method for second order periodic boundary value problems

1983-04-01

S. Leela

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On the validity of the Peano theorem for fuzzy differential equations

1997-03-01

Menahem Friedman , Ming Ma , Abraham Kandel