Positive solutions for double singularly perturbed Schrödinger Maxwell systems. (September 2018)

• Record Type: Journal Article
• Authors: Ghimenti, Marco; Micheletti, Anna Maria
• Is Part Of: Nonlinear analysis. Volume 174(2018)
• Page Start: 223
• Page End: 241
• Publication Date: 2018-09
• Subjects: 35J60 -- 35J47 -- 58E05 -- 81V10; Schrödinger Maxwell systems -- Schrödinger–Poisson–Slater equation -- Singular perturbation -- Lusternik–Schnirelmann category; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2018.05.002
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We show that the number of solutions of a double singularly perturbed Schrödinger Maxwell system on a smooth bounded domain Ω ⊂ R 3 depends on the topological properties of the domain. In particular if Ω is non contractible we obtain cat ( Ω ) + 1 positive solutions. The result is obtained via Lusternik–Schnirelmann category theory.