NONTRIVIAL SOLUTIONS FOR A MIXED BOUNDARY PROBLEM FOR SCHRODINGER EQUATIONS WITH AN EXTERNAL MAGNETIC FIELD

作者：Alves Claudianor O^*; Nemer Rodrigo C M; Soares Sergio H M

来源：Topological Methods in Nonlinear Analysis, 2015, 46(1): 329-362.

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

We study the existence of solutions for a class of nonlinear Schrodinger 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.

• 出版日期2015-9