Description

• Title:
  Solutions for quasilinear elliptic systems with vanishing potentials
• Creator:
  Gheraibia, Billel
• Description:
  In this paper, we study the following strongly coupled quasilinear elliptic system: $$ \begin{cases} -\Delta_{p} u+\lambda a(x)|u|^{p-2}u=\dfrac{\alpha}{\alpha+\beta}|u|^{\alpha-2}u|v|^{\beta}, & x\in {\mathbb R}^{N}, \\[10pt] -\Delta_{p} v+\lambda b(x)|v|^{p-2}v=\dfrac{\beta}{\alpha+\beta}|u|^{\alpha}|v|^{\beta-2}v, & x\in {\mathbb R}^{N}, \\ u,v\in D^{1,p}(\R^{N}), \end{cases} $$% where $N\geq 3$, $\lambda> 0$ is a parameter, $p< \alpha+\beta< p^{*}:={Np}/({N-p})$. Under some suitable conditions which are given in section 1, we use variational methods to obtain both the existence and multiplicity of solutions for the system on an appropriated space when the parameter $\lambda$ is sufficiently large. Moreover, we study the asymptotic behavior of these solutions when \hbox{$\lambda\rightarrow\infty$}.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2019 Topological Methods in Nonlinear Analysis
• Date:
  2019.07.13
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 54, No 1 (September 2019); 153 - 175;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2019.032/18001 ;https://apcz.umk.pl/TMNA/article/view/TMNA.2019.032/18002
• Subject:
  Positive solutions;
  potential well;
  quasilinear elliptic systems;
  Primary;
  35H30;
  35J20;
  Secondary;
  35J45
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2019.032
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other