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



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.


Nonlinear Schrodinger equation, variational methods, Lusternik--Schnirelman category, Morse theory

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