Description

• Title:
  Multiple solutions for quasilinear equation involving Hardy critical Sobolev exponents
• Creator:
  Gao, Fengshuang;
  Guo, Yuxia
• Description:
  We consider the following quasilinear elliptic equation with critical Sobolev and Hardy-Sobolev exponents: \[ \begin{cases} \displaystyle -\sum\limits_{i,j=1}^ND_j(b_{ij}(v)D_iv)+\frac{1}{2}\sum\limits_{i,j=1}^N b_{ij}'(v)D_ivD_jv \\ \displaystyle \qquad\quad =\frac{|v|^{2^*_sq-2}v}{|x|^s}+\mu|v|^{2^*q-2}v+a(x)|v|^{2q-2}v &\hbox{in }\Omega,\\ v=0 &\hbox{on } \partial\Omega, \end{cases} \] where $b_{ij}\in C^1(\mathbb{R},\mathbb{R})$ satisfies the growth condition $|b_{ij}(t)|\sim|t|^{2(q-1)}$ at infinity, $q\geq1$, $\mu\geq0$, $0< s< 2$, $2^*_s={2(N-s)}/({N-2})$, $2^*={2N}/({N-2})$, $0\in\overline{\Omega}$ and $\Omega$ is a bounded domain in $\mathbb{R}^N$. In this paper, we will investigate the effects of the lower order terms $a(x)|v|^{2q-2}v$ and the growth of $b_{ij}(v)$ at infinity on the existence of infinitely many solutions for the above equations.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2020 Topological Methods in Nonlinear Analysis
• Date:
  2020.05.30
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 56, No 1 (September 2020); 31 - 61;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2019.117/25738 ;https://apcz.umk.pl/TMNA/article/view/TMNA.2019.117/25739
• Subject:
  Quasilinear equation;
  critical Hardy-Sobolev exponent;
  multiple solutions;
  Primary;
  35J62;
  35J20;
  Secondary;
  35B33;
  35J75
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2019.117
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other