Existence of solutions for fractional Schrödinger equation with asymptotically periodic terms
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Authors
Da-Bin Wang
- Department of Applied Mathematics, Lanzhou University of Technology, 730050 Lanzhou, People’s Republic of China.
Man Guo
- Department of Applied Mathematics, Lanzhou University of Technology, 730050 Lanzhou, People’s Republic of China.
Wen Guan
- Department of Applied Mathematics, Lanzhou University of Technology, 730050 Lanzhou, People’s Republic of China.
Abstract
In this paper, we investigate the following nonlinear fractional Schr¨odinger equation
\[(-\Delta)^su + V(x)u = f(x, u), x \in \mathbb{R}^N,\]
where \(s \in (0, 1),N > 2\) and \((-\Delta)^s\) is fractional Laplacian operator. We prove that the problem has a non-trivial solution under
asymptotically periodic case of \(V\) and \(f\) at infinity. Moreover, the nonlinear term \(f\) does not satisfy any monotone condition and
Ambrosetti-Rabinowitz condition.
Share and Cite
ISRP Style
Da-Bin Wang, Man Guo, Wen Guan, Existence of solutions for fractional Schrödinger equation with asymptotically periodic terms, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 2, 625--636
AMA Style
Wang Da-Bin, Guo Man, Guan Wen, Existence of solutions for fractional Schrödinger equation with asymptotically periodic terms. J. Nonlinear Sci. Appl. (2017); 10(2):625--636
Chicago/Turabian Style
Wang, Da-Bin, Guo, Man, Guan, Wen. "Existence of solutions for fractional Schrödinger equation with asymptotically periodic terms." Journal of Nonlinear Sciences and Applications, 10, no. 2 (2017): 625--636
Keywords
- asymptotically periodic
- Fractional Schrödinger equation
- variational method.
MSC
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