Schrödinger-Maxwell systems on Hadamard manifolds

2016/02/11 by Csaba Farkas, Alexandru Kristály, Farkas, Csaba +1
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1602.03704

openalex publication_date 2016/02/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we study nonlinear Schrödinger-Maxwell systems on n-dimensional Hadamard manifolds, 3≤ n≤ 5. The main difficulty resides in the lack of compactness of such manifolds which is recovered by exploring suitable isometric actions. 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.

Citations

• Comparison theorems in Finsler geometry and their applications

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