Systems of coupled Schrodinger equations with sign-changing nonlinearities via classical Nehari manifold approach

We propose existence and multiplicity results for the system of Schrodinger equations with sign-changing nonlinearities in bounded domains or in the whole space . In the bounded domain we utilize the classical approach via the Nehari manifold, which is (under our assumptions) a differentiable manifold of class and the Fountain theorem by Bartsch. In the space we additionally need to assume the -periodicity of potentials and our proofs are based on the concentration-compactness lemma by Lions and the Lusternik-Schnirelmann values.