Systems of coupled Schrödinger equations with sign-changing nonlinearities via classical Nehari manifold approach. Issue 7 (3rd July 2019)

• Record Type: Journal Article
• Authors: Bieganowski, Bartosz
• Is Part Of: Complex variables and elliptic equations. Volume 64:Issue 7(2019)
• Page Start: 1237
• Page End: 1256
• Publication Date: 2019-07-03
• Subjects: A. Pankov; Ground state -- variational methods -- system of Schrödinger equations -- Nehari manifold -- periodic potential; Primary: 35Q60 -- Secondary: 35J20 -- 35Q55 -- 58E05 -- 35J47; Functions of complex variables -- Periodicals; Differential equations, Elliptic -- Periodicals; 515.905
• DOI: 10.1080/17476933.2018.1514029
• Languages: English
• ISSNs: 1747-6933

Abstract

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.