GROUND STATE SOLUTIONS FOR ASYMPTOTICALLY PERIODIC LINEARLY COUPLED SCHRODINGER EQUATIONS WITH CRITICAL EXPONENT

We consider the following system of coupled nonlinear Schrodinger equations { -Delta u + a(x)u = vertical bar u vertical bar(p-2) u + lambda(x)nu, x epsilon R-N, -Delta v + b(x)v = vertical bar v vertical bar(2*-2) v + lambda(x)u, x epsilon R-N, u,v epsilon H-1 (R-N), where N >= 3, 2 < p < 2*, 2* = 2N/(N - 2) is the Sobolev critical exponent, a,b,lambda epsilon C(R-N, R) boolean AND L-infinity (R-N, R) and a(x), b(x) and lambda(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 lambda. In particular, the common condition that vertical bar lambda(x)vertical bar < root a(x)b(x) for all x epsilon R-N is not required.