Description

• Title:
  Existence and concentration of ground state sign-changing solutions for Kirchhoff type equations with steep potential well and nonlinearity
• Creator:
  Cheng, Bitao;
  Chen, Jianhua;
  Tang, Xianhua
• Description:
  We study the following class of elliptic equations: \begin{equation*} -\bigg(a+b\int_{{\mathbb R}^3}|\nabla u|^2dx\bigg)\Delta u+\lambda V(x)u=f(u), \quad x\in{\mathbb R}^3, \end{equation*} where $\lambda,a,b> 0$, $V\in \mathcal{C}({\mathbb R}^3,{\mathbb R})$ and $V^{-1}(0)$ has nonempty interior. First, we obtain one ground state sign-changing solution $u_{b,\lambda}$ applying the non-Nehari manifold method. We show that the energy of $u_{b,\lambda}$ is strictly larger than twice that of the ground state solutions of Nehari-type. Next we establish the convergence property of $u_{b,\lambda}$ as $b\searrow0$. Finally, the concentration of $u_{b,\lambda}$ is explored on the set $V^{-1}(0)$ as $\lambda\rightarrow\infty$.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2018 Topological Methods in Nonlinear Analysis
• Date:
  2018.02.12
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 51, No 1 (March 2018); 111 - 133;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2017.062/14214 ;https://apcz.umk.pl/TMNA/article/view/TMNA.2017.062/14215
• Subject:
  Kirchhoff type equation;
  ground state sign-changing solutions;
  non-Nehari manifold method;
  concentration of solutions;
  35J60;
  35J20
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2017.062
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other