Let (M,g) be a smooth, compact Riemannian manifold with smooth boundary, with n = dim M = 2, 3. We suppose the boundary of 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 of M, by means of the Lusternik–Schnirelmann category. Also, these solutions have a unique maximum point that lies on the boundary.

Low energy solutions for singularly perturbed coupled nonlinear systems on a Riemannian manifold with boundary

GHIMENTI, MARCO GIPO;MICHELETTI, ANNA MARIA
2015

Abstract

Let (M,g) be a smooth, compact Riemannian manifold with smooth boundary, with n = dim M = 2, 3. We suppose the boundary of 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 of M, by means of the Lusternik–Schnirelmann category. Also, these solutions have a unique maximum point that lies on the boundary.
Ghimenti, MARCO GIPO; Micheletti, ANNA MARIA
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/748900
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