Nontrivial solutions for a mixed boundary problem for Schrödinger equations with an external magnetic field
DOI:
https://doi.org/10.12775/TMNA.2015.050Keywords
Nonlinear Schrodinger equation, variational methods, Lusternik--Schnirelman category, Morse theoryAbstract
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.Downloads
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2015-09-01
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ALVES, Claudianor Oliveira, NEMER, Rodrigo C. M. and SOARES, Sergio H. Monari. Nontrivial solutions for a mixed boundary problem for Schrödinger equations with an external magnetic field. Topological Methods in Nonlinear Analysis. Online. 1 September 2015. Vol. 46, no. 1, pp. 329 - 362. [Accessed 24 April 2024]. DOI 10.12775/TMNA.2015.050.
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