Boundary layers to a singularly perturbed Klein–Gordon–Maxwell–Proca system on a compact Riemannian manifold with boundary

Advances in Nonlinear Analysis

article

Mónica Clapp¹  Marco Ghimenti²  Anna Maria Micheletti² 

[1] Instituto de Matemáticas, Universidad Nacional Autónoma de México;Dipartimento di Matematica Applicata, Università di Pisa

关键词: Electrostatic Klein–Gordon–Maxwell–Proca system;    semiclassical limit;    boundary layer;    Riemannian manifold with boundary;    supercritical nonlinearity;    Lyapunov–Schmidt reduction;   

DOI  :  10.1515/anona-2017-0039

学科分类：社会科学、人文和艺术（综合）

来源: De Gruyter

【 摘 要 】

We study the semiclassical limit to a singularly perturbed nonlinear Klein–Gordon–Maxwell–Proca system, with Neumann boundary conditions, on a Riemannian manifold ? {\mathfrak{M}} with boundary. We exhibit examples of manifolds, of arbitrary dimension, on which these systems have a solution which concentrates at a closed submanifold of the boundary of ? {\mathfrak{M}} , forming a positive layer, as the singular perturbation parameter goes to zero. Our results allow supercritical nonlinearities and apply, in particular, to bounded domains in ℝ N {\mathbb{R}^{N}} . Similar results are obtained for the more classical electrostatic Klein–Gordon–Maxwell system with appropriate boundary conditions.

【 授权许可】

CC BY