Existence of solutions to asymptotically periodic Schrodinger equations
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 appl...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2017-01-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2017/15/abstr.html |
| Summary: | 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]. |
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| ISSN: | 1072-6691 |