Multiplicity of nontrivial solutions of semilinear elliptic equations
type: Item
instance of: scholarly article
title: Multiplicity of nontrivial solutions of semilinear elliptic equations
zbMATH Open document ID: 0964.35051
author: Shui-Qiang Liu
author: Chun-Lei Tang
author: Xing-Ping Wu
published in: Journal of Mathematical Analysis and Applications
publication date: 2001-07-02T00:00:00Z
review text: It is considered the following problem: \(-\Delta u = f(x,u)\) in \(\Omega\), \(u=0\) on \(\partial\Omega\), where \(f\) is a subcritical Carathéodory function. It is proved the existence of at least two nontrivial solutions. This paper unifies and generalizes some results from \textit{A. Castro} and \textit{A. C. Lazer} [Ann. Mat. Pura Appl., IV. Ser. 120, 113-137 (1979; Zbl 0426.35038)] as well as from \textit{N. Hirano} and \textit{T. Nishimura} [J. Math. Anal. Appl. 180, No. 2, 566-586 (1993; Zbl 0835.35052)].
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 35B38
Mathematics Subject Classification ID: 35J25
zbMATH DE Number: 1533168
zbMATH Keywords: semilinear elliptic equation
zbMATH Keywords: Dirichlet boundary value problem
zbMATH Keywords: nontrivial solution
zbMATH Keywords: reduction method
zbMATH Keywords: critical point
MaRDI profile type: Publication
full work available at URL: jmaa.2000.6704
OpenAlex ID: W1995311545
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DOI: 10.1006/JMAA.2000.6704
description: scientific article; zbMATH DE number 1533168