Nehari-type ground state solutions for Schrodinger equations including critical exponent

In this paper, we study the following system of nonlinear Schrodinger equations: {-Delta u + a(x)u = vertical bar u vertical bar(p-2)u + lambda(x)upsilon, x is an element of R-N, -Delta upsilon + b(x)upsilon = vertical bar upsilon vertical bar(2*-2)upsilon + lambda(x)u, x is an element of R-N, Where + X(X)11, x E RN, where N >= 3, 2 < p < 2* and 2* = 2N/(N - 2) is the critical Sobolev exponent. Under assumptions that a(x), b(x), lambda(x) is an element of C(R-N, R) are all 1-periodic in each of x(1), x(2),...,x(N) and lambda(2)(x) < a(x)b(x), we prove that the above system has a Nehari-type ground state solution when 0 < a(x) < mu(0) for some mu(0) is an element of (0, 1). (C) 2014 Elsevier Ltd. All rights reserved.