Nontrivial solutions for a mixed boundary problem for Schrödinger equations with an external magnetic field

2013/09/18 by Claudianor Oliveira Alves, Claudianor O. Alves, Alves, Claudianor Oliveira +6
Computer Science · Mathematics · #35A15 #35H30 #35Q55 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics #math.AP #msc:35A15 #msc:35H30 #msc:35Q55

paper · pdf · doi:10.48550/arxiv.1309.4691

This article is based on the second author's doctoral thesis

arxiv created 2013/09/18 · openalex publication_date 2013/09/18 · arxiv updated 2013/09/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the existence of solutions for a class of nonlinear Schrödinger equations involving a magnetic field with mixed Dirichlet-Neumann boundary conditions. We use Lyusternik-Shnirelman category and the Morse theory to estimate the number of nontrivial solutions in terms of the topology of the part of the boundary where the Neumann condition is prescribed.

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