Positive ground state of coupled planar systems of nonlinear Schrodinger equations with critical exponential growth

In this paper, we prove the existence of a positive ground state solution to the following coupled system involving nonlinear Schrodinger equations: ( - Au + V1(x)u = f1(x, u) + lambda(x)v, x E R2, - Av + V2(x)v = f2(x,v) + lambda (x)u, x E R2, where lambda, V1, V2 E C(R2, (0, +infinity)) and f1, f2 : R2 x R-+ R have critical exponential growth in the sense of Trudinger-Moser inequality. The potentials V1(x) and V2(x) sat -O isfy a condition involving the coupling term lambda(x), namely 0 < lambda(x) < lambda 0 V1(x)V2(x). We use non-Nehari manifold, Lions's concentration compactness and strong maximum principle to get a positive ground state solution. Moreover, by using a bootstrap reg-ularity lifting argument and Lq-estimates we get regularity and asymptotic behavior. Our results improve and extend the previous results.