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

Claudianor Oliveira Alves, Rodrigo C. M. Nemer, Sergio H. Monari Soares

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.

Partnerzy platformy czasopism