Description

• Title:
  Multiplicity of positive solutions for Kirchhoff type problems in $\mathbb R^3$
• Creator:
  Hu, Tingxi;
  Lu, Lu
• Description:
  We are concerned with the multiplicity of positive solutions for the following Kirchhoff type problem: \begin{equation*} \begin{cases} \displaystyle - \bigg(\epsilon ^2a + \epsilon b\int_{{\mathbb{R}^3}}{|\nabla u{|^2}} dx \bigg)\Delta u + u = Q(x)|u|^{p-2}u,& x\in \mathbb{R}^3, \hfill \\ u \in H^1(\mathbb{R}^3), \quad u > 0, & x\in \mathbb{R}^3 , \end{cases} \end{equation*} where $\epsilon> 0 $ is a parameter, $a, b> 0$ are constants, $p\in (2, 6)$, and $Q\in C(\mathbb{R}^3)$ is a nonnegative function. We show how the profile of $Q$ affects the number of positive solutions when $\epsilon $ is sufficiently small.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2017 Topological Methods in Nonlinear Analysis
• Date:
  2017.08.19
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 50, No 1 (September 2017); 231 - 252;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2017.028/12630 ;https://apcz.umk.pl/TMNA/article/view/TMNA.2017.028/12631
• Subject:
  Variational method;
  Kirchhoff equation;
  multiplicity of solutions;
  lack of compactness;
  Primary;
  35A15;
  35J20;
  35J60
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2017.028
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other