Existence of solutions for a coupled Schrödinger equations with critical exponent

Abstract

In this paper we study the existence of multiple nontrivial solutions of the coupled Schrödinger system with external sources terms as perturbations. This type of the system arises from Bose-Einstein condensate. As these external sources terms are nonlinear functions and small in some sense, we use fibre map to divide the Nehari manifold into threes parts, and then prove the existence of a nontrivial ground state solution and a bound state solution.

Keywords

• coupled schrödinger equations
• sobolev critical exponent
• variational method
• nehari manifold