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 Schrödinger 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.
math.AP↗