Ground state solutions for asymptotically periodic linearly coupled Schrödinger equations with critical exponent

Abstract

We consider the following system of coupled nonlinear Schrödinger equations

where N ≥ 3, 2 < p < 2*, 2* = 2N/(N-2) is the Sobolev critical exponent, a, b, λ ∈ C(R^N, R) ∩ L^∞(R^N, R) and a(x), b(x) and λ(x) are asymptotically periodic, and can be sign-changing. By using a new technique, we prove the existence of a ground state of Nehari type solution for the above system under some mild assumptions on a, b and λ. In particular, the common condition that |λ(x)| < for all x ∈ R^N is not required.