Positive ground state of coupled systems of Schrödinger equations in involving critical exponential growth

Abstract

In this paper, we study the existence of a positive ground state solution to the following coupled system of nonlinear Schrödinger equations: urn:x-wiley:mma:media:mma4498:mma4498-math-0003 where the nonlinearities f1(x,s) and f2(x,s) are superlinear at infinity and have exponential critical growth of the Trudinger‐Moser type. The potentials V1(x) and V2(x) are nonnegative and satisfy a condition involving the coupling term λ(x), namely, λ(x)2<δ2V1(x)V2(x) for some 0<δ<1. For this purpose, we use the minimization technique over the Nehari manifold and strong maximum principle to get a positive ground state solution. Moreover, by using a bootstrap argument and Lq‐estimates, we get regularity and asymptotic behavior.