Journal
COMPUTERS & MATHEMATICS WITH APPLICATIONS
Volume 74, Issue 6, Pages 1321-1332Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.camwa.2017.06.017
Keywords
Fractional Schrodinger equation; Periodic and asymptotically periodic; Variational methods
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Funding
- NNSF [11601145, 11571370, 11471278]
- Natural Science Foundation of Hunan Province [2017E3130, 2017JJ3131]
- Outstanding youth project of Education Department of Hunan Province [17B143]
- Hunan University of Commerce Innovation Driven Project for Young Teacher [16QD008]
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In this paper, we study the following fractional Schrodinger equation (-Delta)(s)u + V(x)u = f(x,u), x is an element of R-N, where ( -Delta)(s)(s is an element of (0, 1)) denotes the fractional Laplacian. Under some weaker conditions on the nonlinearity, we obtain the existence of solutions for the above problem in periodic case and asymptotically periodic case via variational methods, respectively. (C) 2017 Elsevier Ltd. All rights reserved.
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