GROUND STATES FOR FRACTIONAL SCHRODINGER EQUATIONS WITH ELECTROMAGNETIC FIELDS AND CRITICAL GROWTH  

作　　者：Quanqing LI Wenbo WANG Kaimin TENG Xian WU 李全清;王文波;滕凯民;吴鲜(Department of Mathematics,Honghe University,Mengzi 661100,China;Department of Mathematics and Statistics,Yunnan University,Kunming 650091,China;Department of Mathematics,Taiyuan University of Technology,Taiyuan 030024,China;Department of Mathematics,Yunman Normal University,Kunming 650092,China)

机构地区：[1]Department of Mathematics,Honghe University,Mengzi 661100,China [2]Department of Mathematics and Statistics,Yunnan University,Kunming 650091,China [3]Department of Mathematics,Taiyuan University of Technology,Taiyuan 030024,China [4]Department of Mathematics,Yunman Normal University,Kunming 650092,China

出　　处：《Acta Mathematica Scientia》2020年第1期59-74,共16页数学物理学报（B辑英文版）

基　　金：supported in part by the NationalNatural Science Foundation of China(11801153,11501403,11701322,11561072);the Honghe University Doctoral Research Programs(XJ17B11,XJ17B12,DCXL171027,201810687010);the Yunnan Province Applied Basic Research for Youths(2018FD085);the Yunnan Province Local University(Part)Basic Research Joint Project(2017FH001-013);the Natural Sciences Foundation of Yunnan Province(2016FB011);the Yunnan Province Applied Basic Research for General Project(2019FB001);Technology Innovation Team of University in Yunnan Province。

摘　　要：In this article,we study the following fractional Schrodinger equation with electromagnetic fields and critical growth(-Δ)^sAu+V(x)u=|u|^2^*s-2)u+λf(x,|u|^2)u,x∈R^n,where(-Δ)^sA is the fractional magnetic operator with 0<s<1,N>2s,λ>0,2^*s=2N/(N-2s),f is a continuous function,V∈C(R^n,R)and A∈C(R^n,R^n)are the electric and magnetic potentials,respectively.When V and f are asymptotically periodic in x,we prove that the equation has a ground state solution for largeλby Nehari method.

关 键 词：FRACTIONAL SCHRODINGER EQUATION FRACTIONAL magnetic OPERATOR CRITICAL growth 

分 类 号：O411[理学—理论物理]