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On the number of solutions of NLS equations with magnetics fields in expanding domains |
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| Authors: | Claudianor O. Alves Marcelo F. Furtado |
| Affiliation: | a Universidade Federal da Campina Grande, Departamento de Matemática, 58109-970 Campina Grande, PB, Brazil b Universidade Federal do Pará, Faculdade de Matemática, 66075-110 Belém, PA, Brazil c Universidade de Brasília, Departamento de Matemática, 70910-900 Brasília, DF, Brazil |
| Abstract: | In this paper we look for multiple weak solutions u:Ωλ→C for the complex equation  in Ωλ=λΩ. The set Ω⊂RN is a smooth bounded domain, λ>0 is a parameter, A is a regular magnetic field and f is a superlinear function with subcritical growth. Our main result relates, for large values of λ, the number of solutions with the topology of the set Ω. In the proof we apply minimax methods and Ljusternik-Schnirelmann theory. |
| Keywords: | 35A15 35H30 35Q55 |
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