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

被引：0
|
作者：
崔磊磊 [1 ]
郭佳星 [1 ]
李工宝 [1 ]
机构：
[1] Hubei Key Laboratory of Mathematical Sciences and School of Mathematics and Statistics,Central China Normal University
来源：
Acta Mathematica Scientia | 2023年 / 43卷 / 03期
关键词：
D O I：
暂无
中图分类号：
O175 [微分方程、积分方程];
学科分类号：
070104 ;
摘要：
In this paper, we study the existence and local uniqueness of multi-peak solutions to the Kirchhoff type equations -(ε2a + εb∫R3|?u|2)?u + V(x)u = up, u > 0 in R3,which concentrate at non-degenerate critical points of the potential function V(x), where a, b >0, 1 < p < 5 are constants, and ε > 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{ai}1≤i≤k, where{ai}1≤i≤k are non-degenerate critical points of V(x) as ε→0.
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页码：1131 / 1160
页数：30
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