Description

• Title:
  Positive solution of quasilinear elliptic equations in $\mathbb{R}^N$ with a bounded quasilinearity
• Creator:
  Wu, Maomao;
  Liu, Haidong
• Description:
  Consider the quasilinear elliptic equation $$ -\text{div}(\mathcal{A}(u)\nabla u) +\frac{1}{2}\mathcal{A}'(u)|\nabla u|^2+V(x)u =(I_{\alpha}\ast |u|^p) |u|^{p-2}u\quad \text{in } \R^N, $$% where $\mathcal{A}\in C^1(\R,\R)$ is a positive bounded function, $V$ is a given potential and $I_\alpha$ denotes the Riesz potential with $0< \alpha< N$. While most existing works in the literature are concerned with the case where $\mathcal{A}$ is unbounded, little is known about the case where $\mathcal{A}$ is bounded. Under some general conditions on $\mathcal{A}$ and $V$, we establish the existence of a positive solution for the above equation by variational approach.
• Object availability:
  free access
• Rights: https://creativecommons.org/licenses/by-nd/4.0 ;
  Prawa autorskie (c) 2024 Maomao Wu, Haidong Liu
• Date:
  2024.09.25
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 64, No 2 (December 2024); 675 - 692;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/55390/39868 ;https://apcz.umk.pl/TMNA/article/view/55390/39869
• Subject:
  Quasilinear elliptic equation;
  bounded quasilinearity;
  variational methods;
  Primary: 35J62;
  Secondary: 35A15
• Identifier: https://apcz.umk.pl/TMNA/article/view/55390
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other