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

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