Ground states for Kirchhoff‐type equations with critical or supercritical growth
Quanqing Li, Kaimin Teng, Xian Wu · Mathematical Methods in the Applied Sciences · 2017
In this paper, we study the following Kirchhoff‐type equation with critical or supercritical growth where a>0, b>0, λ>0, p≥6 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 small λ>0 by Nehari method. Moreover, we regard b as a parameter and obtain a convergence property of the ground state solution as b↘0. Our main contribution is related to the fact that we are able to deal with the case p>6.