文献类型：期刊文献

英文题名：On a fractional Schr?dinger equation with periodic potential

作者：Fang, Fei[1]; Ji, Chao[2]

机构：[1] Department of Mathematics, Beijing Technology and Business University, Beijing, 100048, China; [2] Department of Mathematics, East China University of Science and Technology, Shanghai, 200237, China

年份：2019

卷号：78

期号：5

起止页码：1517

外文期刊名：Computers and Mathematics with Applications

收录：EI(收录号：20191406732596)

语种：英文

摘要：In this paper, we first consider the spectrum of the fractional Schr?dinger operator (?Δ)s+V(x) on RN, where s∈(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 (?Δ)s+V(x), we establish an existence result for the fractional Schr?dinger 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. ? 2019