THE LIMITING PROFILE OF SOLUTIONS FOR SEMILINEAR ELLIPTIC SYSTEMS WITH A SHRINKING SELF-FOCUSING CORE  

作　　者：金可 石影 谢华飞 Ke JIN;Ying SHI;Huafei XIE(Zhejiang College,Shanghai University of Finance and Economics,Jinhua,321013,China;School of Mathematical Sciences,Zhejiang Normal University,Jinhua,321004,China;School of Mathematics and Statistics,Nanyang Normal University,Nanyang,473061,China)

机构地区：[1]Zhejiang College,Shanghai University of Finance and Economics,Jinhua,321013,China [2]School of Mathematical Sciences,Zhejiang Normal University,Jinhua,321004,China [3]School of Mathematics and Statistics,Nanyang Normal University,Nanyang,473061,China

出　　处：《Acta Mathematica Scientia》2024年第2期583-608,共26页数学物理学报（B辑英文版）

基　　金：supported by the NSFC (12071438);supported by the NSFC (12201232)

摘　　要：In this paper,we consider the semilinear elliptic equation systems{△u+u=αQ_(n)(x)|u|^(α-2)|v|^(β)u in R^(N),-△v+v=βQ(x)|u|^(α)|v|^(β-2)v in R^(N),where N≥3,α,β>1,α+β<2^(*),2^(*)=2N/N-2 and Q_(n) are bounded given functions whose self-focusing cores{x∈R^(N)|Q_(n)(x)>0} shrink to a set with finitely many points as n→∞.Motivated by the work of Fang and Wang[13],we use variational methods to study the limiting profile of ground state solutions which are concentrated at one point of the set with finitely many points,and we build the localized concentrated bound state solutions for the above equation systems.

关 键 词：Schrödinger system ground states solutions bound state solutions 

分 类 号：O175.25[理学—数学]