Critical and subcritical elliptic systems in dimension two

Djairo G. de Figueiredo, João Marcos do Ó, Bernhard Ruf

Type: Article

Publication Date: 2004-01-01

Citations: 76

DOI: https://doi.org/10.1512/iumj.2004.53.2402

Abstract

In this paper we study the existence of nontrivial solutions for the following system of two coupled semilinear Poisson equations:where Ω is a bounded domain in R 2 with smooth boundary ∂Ω, and the functions f and g have the maximal growth which allow us to treat problem (S) variationally in the Sobolev space H 1 0 (Ω).We consider the case with nonlinearities in the critical growth range suggested by the so-called Trudinger-Moser inequality.

Locations

Indiana University Mathematics Journal - View
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Works Cited by This (9)

Action	Title	Year	Authors
+	Multiplicity results for semilinear elliptic equations in a bounded domain of $\mathbb {R}^2$ involving critical exponents	1990	Adimurthi S. L. Yadava
+	Convex functions and Orlicz spaces	1961	M. A. Krasnosel’skii I︠a︡. B. Rutit︠s︡kiĭ Leo F. Boron
+ PDF Chat	Strongly indefinite systems with critical Sobolev exponents	1998	Josephus Hulshof Enzo Mitidieri Robertus C.A.M. Vandervorst
+	Elliptic Equations in R2 with Nonlinearities in the Critical Growth Range	1995	Djairo G. de Figueiredo Olı́mpio H. Miyagaki Bernhard Ruf
+ PDF Chat	On Imbeddings into Orlicz Spaces and Some Applications	1967	Neil S. Trudinger
+	Global Compactness Properties of Semilinear Elliptic Equations with Critical Exponential Growth	2000	Adimurthi Michaël Struwe
+	Minimax Methods in Critical Point Theory with Applications to Differential Equations	1986	P. Rabinowitz
+	On an inequality by N. Trudinger and J. Moser and related elliptic equations	2001	Djairo G. de Figueiredo João Marcos do Ó Bernhard Ruf
+	A sharp form of an inequality by N. Trudinger	1971	J. Moser