Ground state solutions for a quasilinear Kirchhoff type equation

We study the ground state solutions of the following quasilinear Kirchhoff type equation \[ -\left(1+b\int_{\mathbb{R}^{3}}|\nabla u|^2dx\right)\Delta u + V(x)u-[\Delta(u^2)]u=|u|^{10}u+\mu |u|^{p-1}u,\qquad x\in \mathbb{R}^3, \] where $b\geq 0$ and $\mu$ is a positive parameter. Under some suitable...

Full description

Saved in:
Bibliographic Details
Published inElectronic journal of qualitative theory of differential equations Vol. 2016; no. 90; pp. 1 - 14
Main Authors Liu, Hongliang, Chen, Haibo, Xiao, Qizhen
Format Journal Article
LanguageEnglish
Published University of Szeged 01.01.2016
Subjects
ground state solution
kirchhoff type equations
quasilinear
variational methods
Online AccessGet full text

Cover

More Information
Summary:We study the ground state solutions of the following quasilinear Kirchhoff type equation \[ -\left(1+b\int_{\mathbb{R}^{3}}|\nabla u|^2dx\right)\Delta u + V(x)u-[\Delta(u^2)]u=|u|^{10}u+\mu |u|^{p-1}u,\qquad x\in \mathbb{R}^3, \] where $b\geq 0$ and $\mu$ is a positive parameter. Under some suitable conditions on $V(x),$ we obtain the existence of ground state solutions of the above equation with $1<p<11.$
ISSN:1417-3875
1417-3875
DOI:10.14232/ejqtde.2016.1.90