Existence and uniqueness for a Schrödinger system via Nash equilibrium approach

Abstract

In this paper we prove the existence and uniqueness of a solution to a coupled nonlinear Schrödinger system with coercive potentials by characterizing it as a Nash-type equilibrium of the associated energy functionals. Using variational methods and a Perov-type fixed-point argument, we show that the solution operator is a contraction in $H^1\left(R^N\right)\times H^1\left(R^N\right)$, under subcritical growth conditions on the nonlinearities.