Nontrivial solutions for a mixed boundary problem for Schr\"odinger equations with an external magnetic field

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

Nontrivial solutions for a mixed boundary problem for Schr\"odinger equations with an external magnetic field

Analysis of PDEs 2013-09-19 v1

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

Abstract

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.

Keywords

nonlinear schrödinger equations external magnetic field mixed boundary conditions dirichlet-neumann conditions lyusternik-shnirelman category morse theory nontrivial solutions

Cite

@article{arxiv.1309.4691,
  title  = {Nontrivial solutions for a mixed boundary problem for Schr\"odinger equations with an external magnetic field},
  author = {Claudianor Oliveira Alves and Rodrigo Cohen Mota Nemer and Sérgio Henrique Monari Soares},
  journal= {arXiv preprint arXiv:1309.4691},
  year   = {2013}
}

Comments

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

Related papers

View all related →