Existence of infinitely many solutions for a Neumann problem involving the \(p(x)\)-Laplacian
type: Item
instance of: scholarly article
title: Existence of infinitely many solutions for a Neumann problem involving the \(p(x)\)-Laplacian
zbMATH Open document ID: 1157.35040
author: Chao Ji
author: Xianling Fan
published in: Journal of Mathematical Analysis and Applications
publication date: 2007-07-09T00:00:00Z
review text: The authors consider the Neumann problem involving the \(p(x)\)-Laplacian of the type \[ \begin{gathered} -\text{div}(|\nabla u|^{p(x)-2}\nabla u)+ \lambda(x)|u(x)|^{p(x)- 2} u= f(x,u)+ g(x,u)\text{ in }\Omega,\\ {\partial u\over\partial n}= 0\quad\text{on }\partial\Omega,\end{gathered}\tag{1} \] where \(p\in L^\infty(\Omega)\), \(\Omega\subset \mathbb{R}^d\) is a bounded open set with boundary of class \(C^1\), \(n\) is the outward unit normal to the boundary \(\partial\Omega\), and \(p> d\). Using a variational method (under some suitably assumptions on \(p\), \(f\), \(g\)), the authors prove the existence of infinitely many solutions for (1).
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35J20
Mathematics Subject Classification ID: 47J30
Mathematics Subject Classification ID: 49J45
zbMATH DE Number: 5170206
zbMATH Keywords: \(p(x)\)-Laplacian equation
zbMATH Keywords: Neumann problem
zbMATH Keywords: variational principle
zbMATH Keywords: variable exponent Sobolev space
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
full work available at URL: j.jmaa.2006.12.055
OpenAlex ID: W2150036184
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DOI: 10.1016/J.JMAA.2006.12.055
description: scientific article