Existence and non-existence of nontrivial solutions for Schrödinger systems via Nehari-Pohozaev manifold

This paper is concerned with existence of bound states for a coupled gradient system of nonautonomous Schrödinger equations which arises from studies of nonlinear optics and Bose-Einstein condensates. By using variational methods that are constrained to a Nehari-Pohozaev manifold, we obtain existence of nonnegative and positive bound states solutions. In Particular, we show non-existence result for a minimizing problem.