一类带有两个参数的临界薛定谔-泊松方程的多重解  

Multiplicity of Solutions for a Class of Critical Schrodinger-Poisson System with Two Parameters

作　　者：陈永鹏 杨志鹏 Chen Yongpeng;Yang Zhipeng(School of Science,Guangxi University of Science and Technology,Guangxi Liuzhou 545006;Mathematical Institute,Georg-August-University of Gottingen,Gottingen 37073)

机构地区：[1]广西科技大学理学院,广西柳州545006 [2]Georg-August-University of Göttingen,Göttingen 37073

出　　处：《数学物理学报（A辑）》2021年第6期1750-1767,共18页Acta Mathematica Scientia

基　　金：广西高校中青年教师科研基础能力提升项目(2017KY1383,2021KY0348)。

摘　　要：该文研究如下一类临界薛定谔-泊松方程{-△u+λV(x)u+Фu=μu|^(p-2)u+|u|^(4)u,x∈R^(3)-△Ф=u^(2),x∈R^(3),其中λ>0,μ>0是两个参数,p∈(4,6),V满足一些势井条件.当参数λ充分大时,利用变分法证明了基态解的存在性:以及随着λ→∞时,这些解的渐近行为.另外,在参数λ充分大和μ充分小时,利用Ljusternik-Schnirelmann理论,到了多重解的存在性定理.In this paper,we consider the following critical Schrodinger-Poisson system{-△u+λV(x)u+Фu=μu|^(p-2)u+|u|^(4)u,x∈R^(3)-△Ф=u^(2),x∈R^(3),whereλ,μare two positive parameters,p∈(4,6)and V satisfies some potential well conditions.By using the variational arguments,we prove the existence of ground state solutions forλlarge enough andμ>0,and their asymptotical behavior asλ→∞.Moreover,by using LusternikSchnirelmann theory,we obtain the existence of multiple solutions ifλis large andμis small.

关 键 词：临界指标 渐近行为 多重解 

分 类 号：O175.2[理学—数学]