Ground states for Kirchhoff-type equations with critical or supercritical growth

In this paper, we study the following Kirchhoff-type equation with critical or supercritical growth -(a + b integral(R3) vertical bar del u vertical bar(2)dx) Delta u + V(x)u = f (x, u) + lambda vertical bar u vertical bar(p-2)u, x is an element of R-3, where a > 0, b > 0, lambda > 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 lambda > 0 by Nehari method. Moreover, we regard b as a parameter and obtain a convergence property of the ground state solution as b SE arrow 0. Our main contribution is related to the fact that we are able to deal with the case p > 6.