Ground State Solutions of Schrodinger-Kirchhoff Equations with Potentials Vanishing at Infinity

In this paper, we deal with the following Schrodinger-Kirchhoff equation with potentials vanishing at infinity: -(epsilon(2)a + epsilon b integral(R3) vertical bar del u vertical bar(2))Delta u + V(x)u = K(x)vertical bar u vertical bar(p-1)u in R-3 and u > 0, u is an element of H-1 (R-3), where V(x) similar to vertical bar x vertical bar(-alpha) and K(x) similar to vertical bar x vertical bar(-beta) with 0 < alpha < 2, and beta > 0. We first prove the existence of positive ground state solutions u epsilon is an element of H-1 (R-3) under the assumption that sigma < p < 5 for some sigma = sigma(alpha,beta), then we show that u(epsilon) concentrates at a global minimum point of A(x) = V2/(p-1)-1/2(x)/K2/(p-1)(x).