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

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

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...

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Veröffentlicht in:arXiv.org 2013-09
Hauptverfasser: Claudianor Oliveira Alves, Rodrigo Cohen Mota Nemer, Sérgio Henrique Monari Soares
Format: Artikel
Sprache:eng
Schlagworte:
Boundary conditions
Dirichlet problem
Magnetic fields
Mathematical analysis
Nonlinear equations
Schrodinger equation
Topology
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Zusammenfassung: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.
ISSN:2331-8422