摘要
本文将研究以下具有临界频率的分数阶薛定谔-泊松系统:{ε^(2s)(-△)su+V(X)U+k(X)φu=|u|^(2s^(*)-2)ux∈R^3(-△)Sφ=K(x)u^(2)x∈R^(3)其中ε>0是参数,s∈(3/4,1],2s*=6/(3-2s)是分数阶临界指数,K(x)∈L6/(6s-3)(R^(3))是一个非负函数,V(x)∈L3/2s(R^(3))是非负连续位势,假设V(x)在R^(3)的某一区域内为0,这意味着它是临界频率的。通过全局紧引理,两个质心函数和Lusternik-Schnirelman理论,我们证明了高能量半经典基态解的多重性。
In this paper,we study the following fractional Schr?dinger-Poisson System with critical frequency:{ε^(2s)(-△)su+V(X)U+k(X)φu=|u|^(2s^(*)-2)ux∈R^3(-△)Sφ=K(x)u^(2)x∈R^(3)whereε>0 is a parameter,s∈(3/4,1],2s*=6/(3-2s)is the fractional critical exponent,K(x)∈L6/(6s-3)(R^(3))is a nonnegative functions,while V(x)∈L3/2s(R^(3))is a nonnegative continuous potentials and V(x)is assumed to be zero in some region of R^(3),which means it is of the critical frequency case.By virtue of a global compactness lemma,two barycenter functions and Lusternik-Schnirelman theory,we show the multiplicity of high energy semiclassical states.
作者
张鑫瑞
贺小明
屈思琪
ZHANG Xinrui;HE Xiaoming;QU Siqi(School of science,Minzu University of China,Beijing 100081,China)
出处
《中央民族大学学报（自然科学版）》
2021年第1期21-27,共7页
Journal of Minzu University of China(Natural Sciences Edition)
