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.
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)
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。
