Ground state solution of semilinear Schrödinger system with local super-quadratic conditions

Abstract

This paper is dedicated to studying the following semilinear Schrodinger system (-Delta u+ V-1(x)u = F-u(x, u, v) in R-N, - Delta v + V-2(x)v = F-v(x, u, v) in R-N, u, v is an element of H-1(R-N), where the potential Vi are periodic in x, i = 1, 2, the nonlinearity F is assumed to be super-quadratic at some x is an element of R-N and asymptotically quadratic otherwise. Under a local super-quadratic condition of F, an approximation argument and variational method are used to prove the existence of Nehari-Pankov type ground state solutions and the least energy solutions.