Ground state solutions for a quasilinear Kirchhoff type equation

Abstract

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 $1<p<11.$

Keywords

• kirchhoff type equations
• ground state solution
• quasilinear
• variational methods