Systems of coupled Schrödinger equations with sign-changing nonlinearities via classical Nehari manifold approach. Issue 7 (3rd July 2019) - Bieganowski, Bartosz
ABSTRACT: We propose existence and multiplicity results for the system of Schrödinger equations with sign-changing nonlinearities in bounded domains or in the whole spaceR N . In the bounded domain we utilize the classical approach via the Nehari manifold, which is (under our assumptions) a differentiable manifold of classC 1 and the Fountain theorem by Bartsch. In the spaceR N we additionally need to assume theZ N -periodicity of potentials and our proofs are based on the concentration-compactness lemma by Lions and the Lusternik-Schnirelmann values.