Low energy solutions for singularly perturbed coupled nonlinear systems on a Riemannian manifold with boundary. (June 2015)

• Record Type: Journal Article
• Authors: Ghimenti, Marco; Micheletti, Anna Maria
• Is Part Of: Nonlinear analysis. Volume 119(2015)
• Page Start: 315
• Page End: 329
• Publication Date: 2015-06
• Subjects: 35J60 -- 35J20 -- 53C80 -- 81V10; Riemannian manifolds with boundary -- Klein–Gordon–Maxwell systems -- Schroedinger–Maxwell systems -- Lusternik–Schnirelmann category -- One peak solutions; 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.2014.10.024
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: Let ( M, g ) be a smooth, compact Riemannian manifold with smooth boundary, with n = dim M = 2, 3 . We suppose the boundary ∂ M to be a smooth submanifold of M with dimension n − 1 . We consider a singularly perturbed nonlinear system, namely Klein–Gordon–Maxwell–Proca system, or Klein–Gordon–Maxwell system of Schroedinger–Maxwell system on M . We prove that the number of low energy solutions, when the perturbation parameter is small, depends on the topological properties of the boundary ∂ M, by means of the Lusternik–Schnirelmann category. Also, these solutions have a unique maximum point that lies on the boundary.