Ground states for Kirchhoff-type equations with critical growth

In this paper, we study the following Kirchhoff-type equation with critical growth -(a + b integral(3)(R) vertical bar del vertical bar(2)dx)Delta u + V(x)u = lambda f(x,u) + vertical bar u vertical bar(4)u, x is an element of R-3, where a > 0, b > 0, lambda > 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 lambda 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.