Description

• Title:
  Existence of solutions for $p(x)$-Laplacian problem on an unbounded domain
• Creator:
  Yongqiang, Fu
• Description:
  In this paper we study the following $p(x)$-Laplacian problem: $$ \alignat 2 -\div(a(x)|\nabla u|^{p(x)-2}\nabla u)+b(x)|u|^{p(x)-2}u&=f(x,u) &\quad& x\in \Omega,\\ u&=0 &\quad&\text{on }\partial\Omega, \endalignat $$ where $1< p_{1}\le p(x)\le p_{2}< n$, $\Omega\subset {\mathbb R}^{n}$ is an exterior domain. Applying Mountain Pass Theorem we obtain the existence of solutions in $W_{0}^{1,p(x)}(\Omega)$ for the $p(x)$-Laplacian problem in the superlinear case.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Date:
  2007.12.01
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 30, No 2 (December 2007); 235 - 250;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2007.028/8843
• Subject:
  Existence;
  p(x)-Laplacian problem;
  unbounded domain;
  Primary 35J05;
  Secondary 35D05;
  46N20
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2007.028
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other