Two positive nontrivial solutions for a class of semilinear elliptic variational systems

Abstract

We obtain existence and localization results of positive nontrivial solutions for a class of semilinear elliptic variational systems. The proof is based on variants of Schechter’s localized critical point theorems for Hilbert spaces not identified to their duals and on the technique of inverse-positive matrices. The Leray–Schauder boundary condition is also involved.

Authors

Radu Precup
Department of Mathematics, Babes-Bolyai University, Cluj-Napoca, Romania

Keywords

Elliptic system; Positive solution; Critical point; Mountain pass lemma; Leray–Schauder condition; Inverse-positive matrix

Paper coordinates

R. Precup, Two positive nontrivial solutions for a class of semilinear elliptic variational systems, J. Math. Anal. Appl. 373 (2011), 138-146, https://doi.org/10.1016/J.JMAA.2010.06.050

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About this paper

Journal

Journal of Mathematical Analysis and Applications

Publisher Name

Elsevier

Print ISSN
Online ISSN

0022-247X

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