Non-Nehari manifold method for a semilinear Schrödinger equation with critical Sobolev exponent

We consider the semilinear Schrödinger equation {−Δu+V(x)u=K(x)|u|2∗−2u+f(x;u);x∈RN,u∈H1(RN), where N ≥ 4 , 2 ∗ := 2 N / ( N − 2 ) is the critical Sobolev exponent, V;K; f is 1-periodic in x j for j = 1 ; . . . ; N , f ( x ; u ) is subcritical growth. We develop a direct approach to find ground state solutions of Nehari-Pankov type for the above problem. The main idea is to find a minimizing Cerami sequence for the energy functional outside the Nehari-Pankov manifold by using the diagonal method.