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We consider the semilinear Schrödinger equation { −4 u+ V (x)u = K(x)|u|2−2u+ f(x, u), x ∈ RN , u ∈ H1(RN ), where N ≥ 4, 2∗ := 2N/(N − 2) is the critical Sobolev exponent, V,K, f is 1-periodic in xj 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. c ©2016 All rights reserved.

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