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arXiv:1309.4691 [math.AP]AbstractReferencesReviewsResources

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

Claudianor Oliveira Alves, Rodrigo Cohen Mota Nemer, Sérgio Henrique Monari Soares

Published 2013-09-18Version 1

We study the existence of solutions for a class of nonlinear Schr\"odinger 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.

Comments: This article is based on the second author's doctoral thesis
Categories: math.AP
Subjects: 35A15, 35H30, 35Q55
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