Multiplicity of solutions for nonhomogeneous nonlinear elliptic equations with critical exponents.
type: Item
instance of: scholarly article
title: Multiplicity of solutions for nonhomogeneous nonlinear elliptic equations with critical exponents.
zbMATH Open document ID: 1165.35368
DOI: 10.12775/TMNA.2001.034
author: Norimichi Hirano
published in: Topological Methods in Nonlinear Analysis
publication date: 2002-09-11T00:00:00Z
review text: This paper is devoted to the existence and multiplicity of solutions of problem \[ -\Delta u=u^{2^*-2}u+f \quad\text{in }\Omega, \qquad u>0 \quad\text{in }\Omega, \qquad u=0 \quad\text{on }\partial\Omega, \tag{1} \] where \(2^*:=\frac{2N}{N-2}\) is the critical Sobolev exponent, \(N\geq 3\), \(f\in C(\overline{\Omega})\) with \(f\not\equiv 0\) and \(f\geq 0\) on \(\Omega\). Here \(\Omega\) is a bounded domain in \(\mathbb R^N\) with smooth boundary. The author investigates the effect of the topology of \(\Omega\) on the multiple existence of solutions.
reviewed by: Messoud Efendiev
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35B33
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 47J30
zbMATH DE Number: 1799623
zbMATH Keywords: homology groups
MaRDI profile type: Publication
full work available at URL: tmna.2001.034
OpenAlex ID: W2546689205
description: scientific article; zbMATH DE number 1799623