Existence of multiple solutions to a class of nonlinear Schr\"{o}dinger system with external sources terms

TL;DR

This paper investigates the existence of multiple solutions for a nonlinear Schrödinger system with external source terms, relevant to Bose-Einstein condensates, using variational methods and the Nehari manifold.

Contribution

It establishes the existence of multiple positive solutions for the system with small positive external source terms, a novel application of the Nehari manifold approach.

Findings

Existence of a positive ground state solution.

Existence of a positive bound state solution.

Solutions are obtained under smallness conditions on external sources.

Abstract

We study a class of nonlinear schr\"{o}dinger system with external sources terms as perturbations in order to obtain existence of multiple solutions, this system arises from Bose-Einstein condensates etc..As these external sources terms are positive functions and small in some sense, we use Nehari manifold to get the existence of a positive ground state solution and a positive bound state solution.