Mathematics › Applied Mathematics

Differential Equations and Boundary Problems

Works Count: 43632

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Description

This cluster of papers focuses on the study of nonlocal partial differential equations and boundary value problems, including topics such as solvability, numerical solutions, inverse problems, and the behavior of hyperbolic and parabolic equations with nonlocal conditions. The research also delves into the analysis of integro-differential equations and the properties of Green functions.

Keywords

Nonlocal; Partial Differential Equations; Boundary Value Problems; Inverse Problem; Solvability; Numerical Solution; Hyperbolic Equations; Parabolic Equations; Integro-Differential Equations; Green Function

Existence and regularity for a minimum problem with free boundary.

1981-06-01

Hans Wilhelm Alt , Luis Caffarelli

Elliptic Boundary Value Problems in Domains with Point Singularities

2002-11-15

V. A. Kozlov , Vladimir Maz’ya , J. Roßmann

Introduction Part 1: Boundary value problems for ordinary differential equations on the half-axis Elliptic boundary value problems in the half-space Elliptic boundary value problems in smooth domains Variants and extensions … Introduction Part 1: Boundary value problems for ordinary differential equations on the half-axis Elliptic boundary value problems in the half-space Elliptic boundary value problems in smooth domains Variants and extensions Part 2: Elliptic boundary value problems in an infinite cylinder Elliptic boundary value problems in domains with conical points Elliptic boundary value problems in weighted Sobolev spaces with nonhomogeneous norms Variants and extensions Part 3 Elliptic boundary value problems in domains with exterior cusps Elliptic boundary value problems in domains with inside cusps Bibliography Index List of symbols.

Monotone Operators in Banach Space and Nonlinear Partial Differential Equations

2013-02-22

R. E. Showalter

PDE examples by type Linear problems...An introduction Nonlinear stationary problems Nonlinear evolution problems Accretive operators and nonlinear Cauchy problems Appendix Bibliography Index. PDE examples by type Linear problems...An introduction Nonlinear stationary problems Nonlinear evolution problems Accretive operators and nonlinear Cauchy problems Appendix Bibliography Index.

COMPUTATION OF COMBINED REFRACTION - DIFFRACTION

1972-01-29

J.C.W. Berkhoff

This paper treats the derivation of a two-dimensional differential equation, which describes the phenomenon of combined refraction - diffraction for simple harmonic waves, and a method of solving this equation. … This paper treats the derivation of a two-dimensional differential equation, which describes the phenomenon of combined refraction - diffraction for simple harmonic waves, and a method of solving this equation. The equation is derived with the aid of a small parameter development, and the method of solution is based on the finite element technique, together with a source distribution method.

Stability of Solutions of Differential Equations in Banach Space

2002-03-15

Ju. Daleckiĭ , M. Г. Крейн

Methods for Solving Incorrectly Posed Problems

1984-01-01

Vladimir A. Morozov

Non-negative solutions of linear parabolic equations

1968-01-01

D. G. Aronson

Complex powers of an elliptic operator

1967-01-01

R. Seeley

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Asymptotic Theory of Certain "Goodness of Fit" Criteria Based on Stochastic Processes

1952-06-01

T. W. Anderson , D. A. Darling

The statistical problem treated is that of testing the hypothesis that $n$ independent, identically distributed random variables have a specified continuous distribution function $F(x)$. If $F_n(x)$ is the empirical cumulative … The statistical problem treated is that of testing the hypothesis that $n$ independent, identically distributed random variables have a specified continuous distribution function $F(x)$. If $F_n(x)$ is the empirical cumulative distribution function and $\psi(t)$ is some nonnegative weight function $(0 \leqq t \leqq 1)$, we consider $n^{\frac{1}{2}} \sup_{-\infty<x<\infty} \{| F(x) - F_n(x) | \psi^\frac{1}{2}\lbrack F(x) \rbrack\}$ and $n\int^\infty_{-\infty}\lbrack F(x) - F_n(x) \rbrack^2 \psi\lbrack F(x)\rbrack dF(x).$ A general method for calculating the limiting distributions of these criteria is developed by reducing them to corresponding problems in stochastic processes, which in turn lead to more or less classical eigenvalue and boundary value problems for special classes of differential equations. For certain weight functions including $\psi = 1$ and $\psi = 1/\lbrack t(1 - t) \rbrack$ we give explicit limiting distributions. A table of the asymptotic distribution of the von Mises $\omega^2$ criterion is given.

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Regularity for a more general class of quasilinear elliptic equations

1984-01-01

Peter Tolksdorf

Combined Effects of Concave and Convex Nonlinearities in Some Elliptic Problems

1994-06-01

Antonio Ambrosetti , Haïm Brézis , G. Cerami

On some non-linear elliptic differential-functional equations

1966-01-01

Philip Hartman , Guido Stampacchia

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Boundary Value Problems for Operator Differential Equations

1991-01-01

В. И. Горбачук , М. Л. Горбачук

Boundary problems for pseudo-differential operators

1971-01-01

L. Boutet de Monvel

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Aggregation of Variables in Dynamic Systems

1977-01-01

Herbert A. Simon

On solutions of δu=f(u)

1957-01-01

Joachim Keller

Bifurcation, perturbation of simple eigenvalues, itand linearized stability

1973-06-01

Michael G. Crandall , Paul H. Rabinowitz

Linear and Quasi-linear Equations of Parabolic Type

1968-12-31

O. Ladyženskaja , V. A. Solonnikov , N. Ural’ceva

Introductory material Auxiliary propositions Linear equations with discontinuous coefficients Linear equations with smooth coefficients Quasi-linear equations with principal part in divergence form Quasi-linear equations of general form Systems of linear … Introductory material Auxiliary propositions Linear equations with discontinuous coefficients Linear equations with smooth coefficients Quasi-linear equations with principal part in divergence form Quasi-linear equations of general form Systems of linear and quasi-linear equations Bibliography.

On the solution of nonlinear hyperbolic differential equations by finite differences

1952-08-01

Richard Courant , Eugene Isaacson , Mina Rees

A classification of solutions of a conformally invariant fourth order equation in R n

1998-06-30

Chang‐Shou Lin

In this paper, we consider the following conformally invariant equations of fourth order \begin{cases} \Delta^2 u = 6 e^{4u} & \text{in } \mathbf {R}^4, \cr e^{4u} \in L^1(\mathbf {R}^4), \end{cases} … In this paper, we consider the following conformally invariant equations of fourth order \begin{cases} \Delta^2 u = 6 e^{4u} & \text{in } \mathbf {R}^4, \cr e^{4u} \in L^1(\mathbf {R}^4), \end{cases} \qquad (1) and \begin{cases} \Delta^2 u = u^{n+4 \over n-4}, \cr u>0 \quad \text{in } {\mathbf R}^n \quad \text{for } n \ge5 , \cr \end{cases} \quad (2) where \Delta^2 denotes the biharmonic operator in \mathbf{R}^n . By employing the method of moving planes, we are able to prove that all positive solutions of (2) are arised from the smooth conformal metrics on S^n by the stereograph projection. For equation (1), we prove a necessary and sufficient condition for solutions obtained from the smooth conformal metrics on S^4 .

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Uniform asymptotic expansions at a caustic

1966-05-01

Donald Ludwig

Sobolev Spaces of Fractional Order, Nemytskij Operators, and Nonlinear Partial Differential Equations

1996-12-31

Thomas Runst , Winfried Sickel

Note on the Derivatives with Respect to a Parameter of the Solutions of a System of Differential Equations

1919-07-01

T. H. Gronwall

Polyharmonic Boundary Value Problems

2010-01-01

Filippo Gazzola , Hans-Christoph Grunau , Guido Sweers

On a quasi-linear parabolic equation occurring in aerodynamics

1951-10-01

Julian D. Cole

A Treatise on the Theory of Bessel Functions

1944-12-01

H. T. Davis , G. N. Watson

Partial Differential Equations

1969-01-01

Reinier Timman

Approximate Solution of Operator Equations

1972-01-01

M. A. Krasnosel’skii , Gennadi Vainikko , П. П. Забрейко +2 more

The Analysis of Linear Partial Differential Operators I

2003-01-01

Lars Hörmander

Optimal Transport for Applied Mathematicians

2015-01-01

Filippo Santambrogio

This monograph presents a rigorous mathematical introduction to optimal transport as a variational problem, its use in modeling various phenomena, and its connections with partial differential equatio This monograph presents a rigorous mathematical introduction to optimal transport as a variational problem, its use in modeling various phenomena, and its connections with partial differential equatio

Vector-valued Laplace Transforms and Cauchy Problems

2001-01-01

Wolfgang Arendt , C. J. K. Batty , Matthias Hieber +1 more

Linear evolution equations in Banach spaces have seen important developments in the last two decades. This is due to the many different applications in the theory of partial differential equations, … Linear evolution equations in Banach spaces have seen important developments in the last two decades. This is due to the many different applications in the theory of partial differential equations, pr

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Analytic Semigroups and Optimal Regularity in Parabolic Problems

1995-01-01

Alessandra Lunardi

A SINGULAR INTEGRAL EQUATION WITH A GENERALIZED MITTAG LEFFLER FUNCTION IN THE KERNEL

1971-01-01

Tilak Raj Prabhakar

On the Lane–Emden–Matukuma equation −Δu=(1+|x|2)−σuα$-\Delta u = (1+|x|^2){}^{-\sigma } u^\alpha$ in Rn$\mathbf {R}^n$ with σ>1$\sigma >1$

2025-06-25

Cao Thanh Tinh | Mathematische Nachrichten

Abstract Of interest in this work is the following equation: with , , and . Our choice of this mathematical model, called Lane–Emden–Matukuma equation, is to provide a natural interpolation … Abstract Of interest in this work is the following equation: with , , and . Our choice of this mathematical model, called Lane–Emden–Matukuma equation, is to provide a natural interpolation of the Lane–Emden equation corresponding to the case and the Matukuma equation corresponding to the case . This is a continuation of our earlier work in which the case was studied. In this work, we are interested in non‐negative, non‐trivial, ‐solutions to the equation in the case and . Our main result indicates that the equation always admits at least one solution unless , , and for some . Together with the non‐existence in in the linear case with , this implies the stability of the model and , suggested by Matukuma, as it does not admit any solution in the regime and .

Nonlocal problems with $$p(x)$$-triharmonic operators and Neumann boundary conditions

2025-06-25

Adnane Belakhdar | Journal of Elliptic and Parabolic Equations

Entire solutions of the eiconal type partial differential equations in $$\mathbb{C}^2$$

2025-06-25

Lianzhong Yang , Wei Chen , Qing Wang | Analysis Mathematica

Best constants for weighted Hardy inequalities in the exterior of balls and circular cylinders

2025-06-25

Stathis Filippas , Achilles Tertikas | Nonlinear Analysis

Highly Accurate Numerical Method for Solving Fractional Differential Equations with Purely Integral Conditions

2025-06-24

H. M. Ahmed | Fractal and Fractional

The main goal of this paper is to present a new numerical algorithm for solving two models of one-dimensional fractional partial differential equations (FPDEs) subject to initial conditions (ICs) and … The main goal of this paper is to present a new numerical algorithm for solving two models of one-dimensional fractional partial differential equations (FPDEs) subject to initial conditions (ICs) and integral boundary conditions (IBCs). This paper builds a modified shifted Chebyshev polynomial of the second kind (MSC2Ps) basis function that meets homogeneous IBCs, named IMSC2Ps. We also introduce two types of MSC2Ps that satisfy the given ICs. We create two operational matrices (OMs) for both ordinary derivatives (ODs) and Caputo fractional derivatives (CFDs) connected to these basis functions. By employing the spectral collocation method (SCM), we convert the FPDEs into a system of algebraic equations, which can be solved using any suitable numerical solvers. We validate the efficacy of our approach through convergence and error analyses, supported by numerical examples that demonstrate the method’s accuracy and effectiveness. Comparisons with existing methodologies further illustrate the advantages of our proposed technique, showcasing its high accuracy in approximating solutions.

Hyperbolic Stefan problem with nonlocal boundary conditions

2025-06-24

V. M. Kyrylych , Galyna Beregova , Olha Milchenko | Matematychni Studii

In this paper, we consider problems with unknown boundaries for hyperbolic equations and systems with free boundaries with two independent variables. The boundary conditions for such equations in the linear … In this paper, we consider problems with unknown boundaries for hyperbolic equations and systems with free boundaries with two independent variables. The boundary conditions for such equations in the linear or quasilinear cases are given in nonlocal (non-separable and integral) form. The hyperbolic Stefan and Darboux-Stefan problems (the line of initial conditions degenerates to a point) are considered. There are proved the existence and uniqueness theorems of generalized solution, which are continuous solutions of equivalent systems of the second kind Volterra integral equations.The method of characteristics based on a combination of the Banach fixed point theorem allows us to obtain global generalized solutions in terms of the time variable in the case of linear hyperbolic equations with free boundaries and local solutions for quasilinear equations.Nonlocal (non-separable and integral) conditions require additional solvability conditions that are not present in the case of generally accepted boundary conditions for hyperbolic equations and systems. The paper provides examples indicating the significance of the conditions for the solvability of the corresponding problems. The corresponding solutions may have discontinuities along the characteristics of the hyperbolic equations. This additionally requires setting the conditions for matching the initial data of the problems at the corner points of the considered domains.This paper extends the results on the problems with nonlocal conditions for hyperbolic equations and systems to the case of hyperbolic equations with free boundaries.

On Homogeneous Limit Integral Equations of Fredholm Type in Spaces of Bounded Functions

2025-06-24

| Journal of contemporary applied mathematics.

Estimates of Some Dyadic Operators in the Weighted Setting

2025-06-24

Jayadev Nath , Chet Raj Bhatta | Journal of Nepal Mathematical Society

The dyadic square function and the constant Haar multiplier have been estimated linearly with the A₂ characteristic of the weight, [w]_A₂ in the weighted Lebesgue space, L²(w). In this paper, … The dyadic square function and the constant Haar multiplier have been estimated linearly with the A₂ characteristic of the weight, [w]_A₂ in the weighted Lebesgue space, L²(w). In this paper, we explore the estimation of the dyadic variable square function and the estimation of its composition with a constant Haar multiplier. This work shows that, the weight function, w in the dyadic reverse Hölder class 2, RH₂ᵈ, characterizes the boundedness of S_w and S_w∘ T_σ . More precisely, our work is concerned with the boundedness of the dyadic variable square function and the boundedness of its composition from L²(ℝ) to L²(ℝ,w); a single weight case.

Superlinear and Sublinear Dirichlet problems with the (p(y), q(y))-Laplacian operator

2025-06-24

Akanksha Kesarwani , Rasmita Kar | Indian Journal of Pure and Applied Mathematics

Anoverview of complex boundary value problems

2025-06-24

A. Okay Çelebi | Istanbul Journal of Mathematics

The Kato square root problem for parabolic operators with an anti-symmetric part in BMO

2025-06-24

Alireza Ataei , Kaj Nyström | Nonlinear Analysis

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Well-Posedness of Cauchy-Type Problems for Nonlinear Implicit Hilfer Fractional Differential Equations with General Order in Weighted Spaces

2025-06-22

Jakgrit Sompong , Samten Choden , Ekkarath Thailert +1 more | Symmetry

This paper establishes the well-posedness of Cauchy-type problems with non-symmetric initial conditions for nonlinear implicit Hilfer fractional differential equations of general fractional orders in weighted function spaces. Using fixed-point techniques, … This paper establishes the well-posedness of Cauchy-type problems with non-symmetric initial conditions for nonlinear implicit Hilfer fractional differential equations of general fractional orders in weighted function spaces. Using fixed-point techniques, we first prove the existence of solutions via Schaefer’s fixed-point theorem. The uniqueness and Ulam–Hyers stability are then derived using Banach’s contraction principle. By introducing a novel singular-kernel Gronwall inequality, we extend the analysis to Ulam–Hyers–Rassias stability and continuous dependence on initial data. The theoretical framework is unified for general fractional orders and validated through examples, demonstrating its applicability to implicit systems with memory effects. Key contributions include weighted-space analysis and stability criteria for this class of equations.

ON THE SOLVABILITY OF BOUNDARY VALUE PROBLEMS WITH GENERAL CONDITIONS FOR THE TRIHARMONIC EQUATION IN A BALL

2025-06-22

B. D. Koshanov , Nazym Shynybayeva , Мaira Koshanova +1 more | Journal of Mathematics Mechanics and Computer Science

The need to study boundary value problems for elliptic and parabolic equations is dictated by numerous practical applications in the theoretical study of processes in hydrodynamics, electrostatics, mechanics, heat conduction, … The need to study boundary value problems for elliptic and parabolic equations is dictated by numerous practical applications in the theoretical study of processes in hydrodynamics, electrostatics, mechanics, heat conduction, elasticity theory, and quantum physics. This paperinvestigates the solvability of a boundary value problem with general conditions for the triharmonic equation in a unit ball.The validity of the analogue of the Almansi representation is proved. For completeness of presentation, a representation of the Green’s functions of the Dirichlet-2 problem is given. This article indicates the difference between the Green’s function of the real Dirichletproblem and the Green’s function of the Dirichlet-2 problem. It is known that the results of differential equations with partial derivatives in the entire space or differential equations without boundary conditions are in a sense final. The theory of boundary value problems for general differential operators is currently a relevant and rapidly developing part of the theory of differentialequations. However, there is a shortage of explicitly solvable problems on the path of further development of the theory of boundary value problems of differential equations. Over the past decades, sufficient material has been accumulated on the constructive construction of solutions to boundary value problems for model equations with partial derivatives. This article relates to this topical issue.

Investigation of a one-dimensional mixed problem for third order nonlinear differential equations

2025-06-21

Samed Jahangir Aliyev , A. S. Huseynova | European Journal of Technical and Natural Sciences

Reduction Theorems for the Discrete Hardy Operator on Cones of Monotone Sequences

2025-06-21

Амиран Гогатишвили , Nurzhan Bokayev , Gulden Karshygina +2 more | Journal of Mathematical Sciences

Weighted Estimates for Some Schrodinger Type Operators on Spaces of Homogeneous Type

2025-06-20

Haibo Lin , Yecun Wu | Analysis and Applications

Nevanlinna-Pick Interpolation in the Right Half-Plane

2025-06-20

Sameer Chavan , Chaman Kumar Sahu | Complex Analysis and Operator Theory

Publisher Correction: Five Open Problems on the Dirichlet-to-Neumann Operator with Variable Coefficients

2025-06-19

A. F. M. ter Elst , El Maati Ouhabaz | Integral Equations and Operator Theory

On solvability of a nonlocal problem with integral conditions for hyperbolic equation in characteristic domain

2025-06-19

Л. С. Пулькина , A. N. Smirnova | Vestnik of Samara University Natural Science Series

In this article, we study a nonlocal problem for hyperbolic equation in characteristic domain. Additional information on desired solution is given in the form of integrals. This implies that classical … In this article, we study a nonlocal problem for hyperbolic equation in characteristic domain. Additional information on desired solution is given in the form of integrals. This implies that classical methods to justify existence and uniqueness of the solution do not apply. We suggest a slightly different approach. This method enables to find the conditions on data under which the nonlocal problem has at most one solution. We also demonstrate a way to prove the existence of the solution. Moreover, the explicit form of the solution is obtained for certain special case of the equation under consideration

ON DETERMINING HIGHER COEFFICIENT OF A SECOND ORDER HYPERBOLIC EQUATION BY THE VARIATIONAL METHOD

2025-06-19

Hamlet Guliyev , V.N. Nasibzadeh | International Journal of Apllied Mathematics

Observation control problem for differential equations

2025-06-18

B. I. Ananyev | Trudy Instituta Matematiki i Mekhaniki UrO RAN

Mixed Problem for Even-Order Differential Equations with an Involution

2025-06-18

D. M. Polyakov | Владикавказский математический журнал

Initial Boundary Value Problem for a System of Semilinear Parabolic Equations with Absorption and Nonlinear Nonlocal Boundary Conditions

2025-06-18

D. A. Bulyno , Alexander Gladkov , A. I. Nikitin | Владикавказский математический журнал

In this paper we consider classical solutions of an initial boundary value problem for a~system of semilinear parabolic equations with absorption and nonlinear nonlocal boundary conditions. Nonlinearities in equations and … In this paper we consider classical solutions of an initial boundary value problem for a~system of semilinear parabolic equations with absorption and nonlinear nonlocal boundary conditions. Nonlinearities in equations and boundary conditions may not satisfy the Lipschitz condition. To prove the existence of a solution we regularize the original problem. Using the Schauder--Tikhonov fixed point theorem, the existence of a local solution of regularized problem is proved. It is shown that the limit of solutions of the regularized problem is a maximal solution of the original problem. Using the properties of a maximal solution, a comparison principle is proved. In this case, no additional assumptions are made when nonlinearities in absorption do not satisfy the Lipschitz condition. Conditions are found under which solutions are positive functions. The uniqueness of the solution is established. It is shown that the trivial solution $(0, 0 )$ may not be unique.

Criteria for the compact elements in a locally compact group to form a subgroup

2025-06-17

Marwa Gouiaa | Archiv der Mathematik

STUDY OF A VARIANT OF THE HARDY INTEGRAL INEQUALITY

2025-06-17

Christophe Chesneau | Advances in Mathematics Scientific Journal

Non-coercive differential inclusions problems in anisotropic Sobolev spaces with variable exponents

2025-06-17

Mohammed El Ansari , Morad Ouboufettal , Youssef Akdim | Applicable Analysis

Global results for the inhomogeneous Muskat problem

2025-06-16

Neel Patel , Nikhil Shankar | Interfaces and Free Boundaries Mathematical Analysis Computation and Applications

The inhomogeneous Muskat problem models the dynamics of an interface between two fluids of differing characteristics inside a nonuniform porous medium. We consider the case of a porous media with … The inhomogeneous Muskat problem models the dynamics of an interface between two fluids of differing characteristics inside a nonuniform porous medium. We consider the case of a porous media with a permeability jump across a horizontal boundary away from an interface between two fluids of different viscosities and densities. For initial data of explicit medium size, depending on the characteristics of the fluids and porous media, we will prove the global existence and uniqueness of a solution that is instantly analytic and decays in time to the flat interface.

Vanishing Theorems, Support Conditions, and Boundary Problems for $\overline\partial$ on Weak Z(q) Domains

2025-06-16

Sayed Saber , Abdullah Alahmari | International Journal of Analysis and Applications

Let $ X $ be a complex manifold of complex dimension $ n \geq 2 $, and let $ \Omega \Subset \mathcal{X} $ be a relatively compact domain with smooth … Let $ X $ be a complex manifold of complex dimension $ n \geq 2 $, and let $ \Omega \Subset \mathcal{X} $ be a relatively compact domain with smooth boundary that satisfies the weak $ Z(q) $-condition. Assume $ \mathcal{F} $ is a holomorphic line bundle over $ X $, and denote by $ \mathcal{F}^{\otimes m} $ its $ m $-th tensor power for some positive integer $ m $. Provided there exists a strongly plurisubharmonic function defined in a neighborhood of the boundary $ b\Omega $, it is possible to obtain solutions to the $ \overline{\partial} $-equation within $ \Omega $, under support conditions, for $(p,q)$-forms with $ q \geq 1 $ taking values in $ \mathcal{F}^{\otimes m} $. Additionally, we study the solvability of the boundary $ \overline{\partial}_b $-problem on weak $ Z(q) $-domains with smooth boundary in the setting of Kähler manifolds. Moreover, an extension theorem for $ \overline{\partial}_b $-closed differential forms will be proven.

On hybrid fractional differential equations with nonlocal conditions via ABC derivative

2025-06-14

Abderrahim Kraita , Ahmed Hajji | Gulf Journal of Mathematics

In this article, we study the existence of solutions to a fractional hybrid integro-differential equation with nonlocal boundary conditions. Our approach is based on a generalized version of Dhage’s hybrid … In this article, we study the existence of solutions to a fractional hybrid integro-differential equation with nonlocal boundary conditions. Our approach is based on a generalized version of Dhage’s hybrid fixed point theorem, adapted to the sum of three fractional operators. To illustrate the applicability of our main result, we conclude with a concrete example, accompanied by numerical results and graphical representations generated using Python.

Existence, regularity and asymptotic behavior of solutions for a nonlocal Chafee-Infante problem via semigroup theory

2025-06-14

Tomás Caraballo , Alexandre N. Carvalho , Yessica Julio | Topological Methods in Nonlinear Analysis

This article deals with the study of a non-local one-dimensional quasilinear problem with continuous forcing. We use a time-reparameterization to obtain a semilinear problem and study a more general equation … This article deals with the study of a non-local one-dimensional quasilinear problem with continuous forcing. We use a time-reparameterization to obtain a semilinear problem and study a more general equation using semigroup theory. The existence of mild solutions is established without uniqueness with the aid of the formula of variation of constants and asking only a suitable modulus of continuity on the nonlinearity this mild solution is shown to be strong. Comparison results are also established with the aid of the formula of variation of constants and using these comparison results, global existence is obtained with the additional requirement that the nonlinearity satisfy a structural condition. The existence of pullback attractor is also established for the associated multivalued process along with the uniform bounds given by the comparison results with the additional requirement that the nonlinearity be dissipative. As much as possible the results are abstract so that they can be also applied to other models.

A fixed point index approach to a third order nonlocal boundary value problem

2025-06-14

Mirosława Zima , Gabriela Szajnowska | Topological Methods in Nonlinear Analysis

Using a topological approach we study the existence of positive solutions to a third order differential equation subject to nonlocal boundary conditions. Our method is based on the fixed point … Using a topological approach we study the existence of positive solutions to a third order differential equation subject to nonlocal boundary conditions. Our method is based on the fixed point index theory in cones. The main results extend and complement some previous works and are illustrated by suitable examples.

Logarithm singular Dirichlet problem for nonlinear elliptic equations with variable exponent

2025-06-14

Mohamed Bahadi , Akdim Youssef | Gulf Journal of Mathematics

In this paper, we address certain nonlinear problems featuring a logarithm singular source term at the origin within the framework of variable exponent Sobolev spaces. In this paper, we address certain nonlinear problems featuring a logarithm singular source term at the origin within the framework of variable exponent Sobolev spaces.

On the regularity of solutions to a class of nonlocal evolution equations with sectorial operators

2025-06-13

Nguyen Van Dac , Tran Dinh Ke , Pham Anh Toan | Journal of Mathematical Analysis and Applications

Hybrid asymptotic-numerical approaches for solutions of the second-kind Volterra integral equations with highly oscillatory kernels and force terms

2025-06-13

Wei Zhang , Junjie Ma | Journal of Computational and Applied Mathematics

Simulation of solution of hyperbolic equation with Orlicz right side

2025-06-12

B. V. Dovhai | Carpathian Mathematical Publications

The paper is devoted to the construction of a model of a hyperbolic equation solution with a strictly Orlicz random right side and zero initial and boundary conditions. The model … The paper is devoted to the construction of a model of a hyperbolic equation solution with a strictly Orlicz random right side and zero initial and boundary conditions. The model approximates the solution with a given level of reliability and accuracy in the uniform norm.

On the nonlocal noninstataneous Impulsive Integro-differential equations in the frame of a fractional Caputo type derivative

2025-06-12

Mamadou Abdoul Diop , Chaibou Bakar GARBA , Firmin Bodjrenou +1 more | Journal of fractional calculus and applications /Journal of fractional calculus and applications

Boundary Value Problems for Linear and Nonlinear Second Order Ordinary Differential Equations with Involutions

2025-06-12

Abdissalam Sarsenbi , Abdizhahan Sarsenbi , Bolat Seilbekov | Journal of Mathematical Sciences

On a nonlocal problem of Bitsadze{Samarskii type for an elliptic equation with degeneration

2025-06-11

B.J. Kadirkulov , Okiljon Ergashev | Uzbek Mathematical Journal

In this paper, a nonlocal problem of the BitsadzeSamarskii type is studied for a degenerate elliptic equation in a vertical half-strip Ω = f(x; y) : 0 < x < … In this paper, a nonlocal problem of the BitsadzeSamarskii type is studied for a degenerate elliptic equation in a vertical half-strip Ω = f(x; y) : 0 < x < 1; y > 0g. The problem connects the value of the sought function on the right boundary of the domain with its value at an interior point of the same domain. Under certain conditions on the given functions, theorems on the existence and uniqueness of the solution are proved. The uniqueness of the solution is proved using the maximum principle, while the existence of a solution is established by methods of separation of variables and integral equations.