POSITIVE SOLUTIONS WITH HIGH ENERGY FOR FRACTIONAL SCHRODINGER EQUATIONS  

作　　者：郭青 赵雷嘎 Qing GUO;Leiga ZHAO(College of Science,Minzu University of China,Beijing,100081,China;School of Mathematics and Statistics,Beijing Technology and Business University,Beijing,100048,China)

机构地区：[1]College of Science,Minzu University of China,Beijing,100081,China [2]School of Mathematics and Statistics,Beijing Technology and Business University,Beijing,100048,China

出　　处：《Acta Mathematica Scientia》2023年第3期1116-1130,共15页数学物理学报（B辑英文版）

基　　金：supported by the NNSF of China(12171014, 12271539, 12171326);the Beijing Municipal Commission of Education (KZ202010028048);the Research Foundation for Advanced Talents of Beijing Technology and Business University (19008022326)。

摘　　要：In this paper, we study the Schrodinger equations (-△)^(s)u + V(x)u = a(x)|u|^(p-2)u + b(x)|u|^(q-2)u, x∈R^(N),where 0 < s < 1, 2 < q < p < 2_(s)^(*), 2_(s)^(*) is the fractional Sobolev critical exponent. Under suitable assumptions on V, a and b for which there may be no ground state solution, the existence of positive solutions are obtained via variational methods.

关 键 词：fractional Schr?dinger equations positive solution concentration compactness principle 

分 类 号：O175.29[理学—数学]