Description

• Title:
  Existence of positive solution for a class of quasilinear Schrödinger equations with potential vanishing at infinity on nonreflexive Orlicz-Sobolev spaces
• Creator:
  da Silva, Lucas;
  Souto, Marco A. S.
• Description:
  In this paper we investigate the existence of positive solution for a class of quasilinear problem on an Orlicz-Sobolev space that can be nonreflexive $$ - \Delta_{\Phi} u +V(x)\phi(|u|)u= K(x)f(u)\quad\mbox{in } \mathbb{R}^{N}, $$ where $ N \geq 2 $, $ V, K $ are nonnegative continuous functions and $f$ is a continuous function with a quasicritical growth. Here we extend the Hardy-type inequalities presented in \cite{AlvesandMarco} to nonreflexive Orlicz spaces. Through inequalities together with a variational method for non-differentiable functionals we will obtain a ground state solution. We analyze also the problem with $V=0$.
• Object availability:
  free access
• Rights: https://creativecommons.org/licenses/by-nd/4.0 ;
  Prawa autorskie (c) 2024 Lucas da Silva, Marco A. S. Souto
• Date:
  2024.09.21
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 64, No 1 (September 2024); 201 - 241;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/55333/39770 ;https://apcz.umk.pl/TMNA/article/view/55333/39771
• Subject:
  Orlicz-Sobolev spaces;
  variational methods;
  quasilinear elliptic problems;
  $\Delta_{2}$-condition;
  Primary: 35J15, 35J20, 35J62;
  Secondary: 46E30
• Identifier: https://apcz.umk.pl/TMNA/article/view/55333
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other