Schrödinger–Maxwell systems on non-compact Riemannian manifolds. (October 2016)

• Record Type: Journal Article
• Authors: Farkas, Csaba; Kristály, Alexandru
• Is Part Of: Nonlinear analysis. Volume 31(2016)
• Page Start: 473
• Page End: 491
• Publication Date: 2016-10
• Subjects: Schrödinger–Maxwell system -- Riemannian manifold -- Non-compact -- Isometry -- Existence -- Multiplicity; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2016.03.004
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: In this paper we study nonlinear Schrödinger–Maxwell systems on n -dimensional non-compact Riemannian manifolds of Hadamard type, 3 ≤ n ≤ 5 . The main difficulty resides in the lack of compactness which is recovered by exploring suitable isometric actions of the Hadamard manifolds. By combining variational arguments, some existence, uniqueness and multiplicity of isometry-invariant weak solutions are established for the Schrödinger–Maxwell system depending on the behavior of the nonlinear term.