Multiple solutions of degenerate perturbed elliptic problems involving a subcritical Sobolev exponent
type: Item
instance of: scholarly article
title: Multiple solutions of degenerate perturbed elliptic problems involving a subcritical Sobolev exponent
zbMATH Open document ID: 0979.35055
DOI: 10.12775/TMNA.2000.021
published in: Topological Methods in Nonlinear Analysis
publication date: 2002-02-13T00:00:00Z
review text: The authors study the degenerate elliptic equation \[ -\text{div}(a(x)\nabla u)+ b(x)u=K(x) |u|^{p-2}u +g(x) \quad \text{in} \mathbb{R}^N, \] where \(N\geq 2\) and \(2<p<2N/(N-2).\) Under suitable assumptions on the functions \(a,\) \(b\), and \(K\) it is proved that if the perturbation \(g\) is sufficiently small than the above problem has at least two distinct solutions in an appropriate weighted Sobolev space.
Mathematics Subject Classification ID: 35J70
Mathematics Subject Classification ID: 35B20
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 58E05
Mathematics Subject Classification ID: 58E30
zbMATH DE Number: 1545377
zbMATH Keywords: degenerate elliptic problem
zbMATH Keywords: weighted Sobolev space
zbMATH Keywords: unbounded domain
zbMATH Keywords: perturbation
zbMATH Keywords: multiple solutions
author: Florica C. Cîrstea
author: Vicenţiu D. Rădulescu
reviewed by: Lubomira Softova
MaRDI profile type: Publication
full work available at URL: tmna.2000.021
OpenAlex ID: W2548886979
description: scientific article; zbMATH DE number 1545377