THE EXISTENCE AND LOCAL UNIQUENESS OF MULTI-PEAK SOLUTIONS TO A CLASS OF KIRCHHOFF TYPE EQUATIONS  

作　　者：崔磊磊 郭佳星 李工宝 Leilei CUI;Jiaxing GUO;Gongbao LI(Hubei Key Laboratory of Mathematical Sciences and School of Mathematics and Statistics,Central China Normal University,Wuhan,430079,China)

机构地区：[1]Hubei Key Laboratory of Mathematical Sciences and School of Mathematics and Statistics,Central China Normal University,Wuhan,430079,China

出　　处：《Acta Mathematica Scientia》2023年第3期1131-1160,共30页数学物理学报（B辑英文版）

基　　金：supported by the Natural Science Foundation of China(11771166,12071169);the Hubei Key Laboratory of Mathematical Sciences and Program for Changjiang Scholars and Innovative Research Team in University#IRT17R46。

摘　　要：In this paper,we study the existence and local uniqueness of multi-peak solutions to the Kirchhoff type equations-(ε^(2)a+εb∫_(R^(3))|■u|^(2))△u+V(x)u=u^(p),u>0 in R^(3),which concentrate at non-degenerate critical points of the potential function V(x),where a,b>0,1<p<5 are constants,andε>0 is a parameter.Applying the Lyapunov-Schmidt reduction method and a local Pohozaev type identity,we establish the existence and local uniqueness results of multi-peak solutions,which concentrate at{a_(i)}1≤i≤k,where{a_(i)}1≤i≤k are non-degenerate critical points of V(x)asε→0.

关 键 词：Kirchhoff type equations potential functions having non-degenerate critical points the Lyapunov-Schmidt reduction method multi-peak solutions existence and local uniqueness 

分 类 号：O175[理学—数学]