An asymmetric superlinear elliptic problem at resonance. (January 2015)

• Record Type: Journal Article
• Authors: Recôva, Leandro; Rumbos, Adolfo
• Is Part Of: Nonlinear analysis. Volume 112(2015)
• Page Start: 181
• Page End: 198
• Publication Date: 2015-01
• Subjects: Critical groups -- Resonance -- Morse theory; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2014.09.019
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this article, we study the existence and multiplicity of solutions to the problem { − Δ u = g ( x, u ), in Ω ; u = 0, on ∂ Ω, where Ω is a bounded domain in R N ( N ⩾ 2 ) with smooth boundary, and g : Ω ¯ × R → R is a differentiable function. We will assume that g ( x, s ) has a resonant behavior for large negative values of s and that a Landesman–Lazer type condition is satisfied. We also assume that g ( x, s ) is superlinear, but subcritical, for large positive values of s . We prove the existence and multiplicity of solutions for problem(1.1) by using minimax methods and infinite-dimensional Morse theory.