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In this paper, we study the existence of positive solutions for the following class of nonlocal linearly coupled systems involving Schrödinger equations where denotes the fractional Laplacian, and. The coupling function is a bounded and continuous function which is related with the potentials by , for some. We deal with periodic and asymptotically periodic bounded potentials and. On the nonlinear terms and , we assume 'superlinear' at infinity and at the origin. Employing a variational approach, we obtain existence of bound and ground states solutions without assuming the well-known Ambrosetti–Rabinowitz condition on the nonlinear terms. Furthermore, we give a description of the ground states when the coupling function goes to zero in the norm. [ABSTRACT FROM AUTHOR]

In this paper, we prove the existence of positive ground state solutions to the following class of coupled systems involving nonlinear Schrödinger equations where the nonlinearities and have exponential critical growth of the Trudinger-Moser type. Moreover, the coupling term satisfies . We use the minimization technique over the Nehari manifold and strong maximum principle to get a positive ground state solution. [ABSTRACT FROM AUTHOR]