Electron. J. Differential Equations, Vol. 2017 (2017), No. 15, pp. 1-7.

Existence of solutions to asymptotically periodic Schrodinger equations

Marcelo F. Furtado, Reinaldo de Marchi

We show the existence of a nonzero solution for the semilinear Schrodinger equation $-\Delta u+V(x)u=f(x,u)$. The potential V is periodic and 0 belongs to a gap of $\sigma(-\Delta +V)$. The function f is superlinear and asymptotically periodic with respect to x variable. In the proof we apply a new critical point theorem for strongly indefinite functionals proved in [3].

Submitted July 8, 2016. Published January 13, 2017.
Math Subject Classifications: 35J50, 35J45.
Key Words: Strongly indefinite functionals; Schrodinger equation; asymptotically periodic problem.

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Marcelo F. Furtado
Universidade de Brasília
Departamento de Matemática
70910-900 Brasília-DF, Brazil
email: mfurtado@unb.br
Reinaldo de Marchi
Universidade Federal do Mato Grosso
Departamento de Matemática
78060-900 Cuiabá-MT, Brazil
email: reinaldodemarchi@ufmt.br

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