文献类型：期刊文献

英文题名：On a fractional Schrodinger equation with periodic potential

作者：Fang, Fei[1];Ji, Chao[2]

机构：[1]Beijing Technol & Business Univ, Dept Math, Beijing 100048, Peoples R China;[2]East China Univ Sci & Technol, Dept Math, Shanghai 200237, Peoples R China

年份：2019

卷号：78

期号：5

起止页码：1517

外文期刊名：COMPUTERS & MATHEMATICS WITH APPLICATIONS

收录：;WOS:【SCI-EXPANDED(收录号:WOS:000482248100022)】；

基金：The first author is supported by Beijing Municipal Natural Science Foundation (No. 1172005) and NSFC (No. 11801017). The second author is supported by Shanghai Natural Science Foundation Project (18ZR1409100), NSFC (No. 11301181) and China Postdoctoral Science Foundation Project.

语种：英文

外文关键词：Spectrum; Fractional Schrodinger equation; Linking theorem; Periodicity

摘要：In this paper, we first consider the spectrum of the fractional Schrodinger operator (-Delta)(s)+ V(x) on R-N, where s is an element of (0, 1) and V(x) be continuous, periodic in x. Using a new nonlocal normal derivative, we prove that the operator has purely continuous spectrum which is bounded below and consists of closed disjoint intervals. Then when 0 belongs to a spectral gap of (-Delta)(s)+ V(x), we establish an existence result for the fractional Schrodinger equation via a new linking theorem. It is worth to mention that the nonlinear term in our problem does not satisfy the periodicity and the existence result is even new for the case s = 1. (C) 2019 Published by Elsevier Ltd.