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

DOI: http://dx.doi.org/10.12775/TMNA.2015.050

#### Abstract

We study the existence of solutions for a class of nonlinear Schr\"{o}dinger equations involving a magnetic field with mixed Dirichlet--Neumann boundary conditions. We use Lusternik--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 Schrodinger equation, variational methods, Lusternik--Schnirelman category, Morse theory

#### Full Text:

Full Text### Refbacks

- There are currently no refbacks.