Description

• Title:
  Nonhomogeneous Dirichlet problems without the Ambrosetti-Rabinowitz condition
• Creator:
  Li, Gang;
  Rădulescu, Vicenţiu D.;
  Repovš, Dušan D.;
  Zhang, Qihu
• Description:
  We consider the existence of solutions of the following $p(x)$-Laplacian Dirichlet problem without the Ambrosetti-Rabinowitz condition: \begin{equation*} \begin{cases} -\mbox{div}\hspace{.07em}(|\nabla u|^{p(x)-2}\nabla u)=f(x,u) &\text{ in }\Omega , \\ u=0 &\text{ on }\partial \Omega .% \end{cases} \end{equation*} We give a new growth condition and we point out its importance for checking the Cerami compactness condition. We prove the existence of solutions of the above problem via the critical point theory, and also provide some multiplicity properties. The present paper extend previous results of Q. Zhang and C. Zhao (Existence of strong solutions of a $p(x)$-Laplacian Dirichlet problem without the Ambrosetti-Rabinowitz condition, \textit{Computers and Mathematics with Applications}, 2015) and we establish the existence of solutions under weaker hypotheses on the nonlinear term.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2017 Topological Methods in Nonlinear Analysis
• Date:
  2017.10.28
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 51, No 1 (March 2018); 55 - 77;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2017.037/13232 ;https://apcz.umk.pl/TMNA/article/view/TMNA.2017.037/13233
• Subject:
  Nonhomogeneous differential operator;
  Ambrosetti-Rabinowitz condition;
  Cerami compactness condition;
  Sobolev space with variable exponent;
  Primary;
  35J60;
  Secondary;
  35J20;
  35J25;
  58E05
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2017.037
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other