Description

• Title:
  Existence of positive ground state solutions for Kirchhoff type equation with general critical growth
• Creator:
  Liu, Zhisu;
  Luo, Chaoliang
• Description:
  We study the existence of positive ground state solutions for the nonlinear Kirchhoff type equation $$ \begin{cases} \displaystyle -\bigg(a+b\int_{\mathbb R^3}|\nabla u|^2\bigg)\Delta {u}+V(x)u =f(u) & \mbox{in }\mathbb R^3, \\ \noalign{\medskip} u\in H^1(\mathbb R^3), \quad u> 0 & \mbox{in } \mathbb R^3, \end{cases} $$% where $a,b> 0$ are constants, $f\in C(\mathbb R,\mathbb R)$ has general critical growth. We generalize a Berestycki-Lions theorem about the critical case of Schrödinger equation to Kirchhoff type equation via variational methods. Moreover, some subcritical works on Kirchhoff type equation are extended to the current critical case.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Date:
  2016.10.17
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 49, No 1 (March 2017); 165 - 182;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2016.068/10147 ;https://apcz.umk.pl/TMNA/article/view/TMNA.2016.068/10148
• Subject:
  Kirchhoff type problem;
  ground state solution;
  variational method;
  Primary;
  35J60;
  35Q51;
  Secondary;
  53C35
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2016.068
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other