Semiclassical solutions for linearly coupled Schrodinger equations without compactness

We consider the following system of singularly perturbed coupled nonlinear Schrodinger equations {-epsilon(2)Delta u + a(x)u = vertical bar u vertical bar(p-2) u + mu(x)v, x is an element of R-N, -epsilon(2)Delta v + b(x)v = vertical bar v vertical bar(q-2)v + mu(x)u, x is an element of R-N, u, v is an element of H-1 (R-N), where N >= 3, 2 < p < 2*, 2 < p <= 2* and a, b, mu is an element of C(R-N), 2* = 2N/(N - 2) is the Sobolev critical exponent. Under assumptions that a(0) = inf a = 0, b(x) >= 0 and vertical bar mu(x)vertical bar(2) <= theta(2)a(x)b(x) with theta is an element of (0, 1), we show that the system has at least one nontrivial solution provided that 0 <= epsilon <= epsilon(0), where the bound is formulated in terms of a, b, and N.