Ground states for Kirchhoff-type equations with critical growth
Quanqing Li, Kaimin Teng, Xian Wei Wu · Communications on Pure & Applied Analysis · 2018
In this paper, we study the following Kirchhoff-type equation with critical growth $-(a+b\int {_{\mathbb{R}^3}} | abla u|^2dx)\triangle u+V(x)u = λ f(x,u)+|u|^4u, \; x \; ∈\mathbb{R}^3,$ where a>0, b>0, λ>0 and f is a continuous superlinear but subcritical nonlinearity. When V and f are asymptotically periodic in x, we prove that the equation has a ground state solution for large λ by Nehari method. Moreover, we regard b as a parameter and obtain a convergence property of the ground state solution as $b\searrow 0$.