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

作者机构：Department of MathematicsHonghe UniversityMengzi 661100China Department of Mathematics and StatisticsYunnan UniversityKunming 650091China Department of MathematicsTaiyuan University of TechnologyTaiyuan 030024China Department of MathematicsYunman Normal UniversityKunming 650092China 

出 版 物：《Acta Mathematica Scientia》 (数学物理学报（B辑英文版）)

年 卷 期：2020年第40卷第1期

页      面：59-74页

核心收录：

学科分类：07[理学] 070201[理学-理论物理] 0702[理学-物理学] 

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 

主　　题：fractional Schrodinger equation fractional magnetic operator critical growth 

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 02s,λ0,2^*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,*** V and f are asymptotically periodic in x,we prove that the equation has a ground state solution for largeλby Nehari method.