ON A CLASS OF LINEARLY COUPLED SYSTEMS ON RN INVOLVING ASYMPTOTICALLY LINEAR TERMS

In this work we study the existence of positive solutions for the following class of coupled elliptic systems involving nonlinear Schrodinger equations {-Delta u + V-1(x)u = f(1)(u) + lambda(x)v, x is an element of R-N, -Delta u + V-2(x)v = f(2)(u) + lambda(x)u, x is an element of R-N, where N >= 3 and the nonlinearities f(1) and f(2) are asymptotically linear at infinity. The potentials V-1(x) and V-2(x) are continuous functions which are bounded from below and above. The function lambda x) is continuous and gives us a linear coupling due the terms lambda(x)u and lambda(x)v. Here we employ some variational arguments jointly with a Pohozaev identity.