THE EXISTENCE AND LOCAL UNIQUENESS OF MULTI-PEAK POSITIVE SOLUTIONS TO A CLASS OF KIRCHHOFF EQUATION

doi:10.1007/s10473-020-0107-y

数学物理学报(英文版) ›› 2020, Vol. 40 ›› Issue (1): 90-112.doi: 10.1007/s10473-020-0107-y

THE EXISTENCE AND LOCAL UNIQUENESS OF MULTI-PEAK POSITIVE SOLUTIONS TO A CLASS OF KIRCHHOFF EQUATION

李工宝, 牛亚慧

Hubei Key Laboratory of Mathematical Sciences and School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China

收稿日期:2018-11-20 修回日期:2019-03-27 出版日期:2020-02-25 发布日期:2020-04-14
通讯作者: Gongbao LI E-mail:ligb@mail.ccnu.edu.cn
基金资助:
This work was supported by Natural Science Foundation of China (11771166), Hubei Key Laboratory of Mathematical Sciences and Program for Changjiang Scholars and Innovative Research Team in University \#IRT_17R46. Niu was financially supported by funding for basic research business in Central Universities (innovative funding projects) (2018CXZZ090).

THE EXISTENCE AND LOCAL UNIQUENESS OF MULTI-PEAK POSITIVE SOLUTIONS TO A CLASS OF KIRCHHOFF EQUATION

Gongbao LI, Yahui NIU

Hubei Key Laboratory of Mathematical Sciences and School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China

Received:2018-11-20 Revised:2019-03-27 Online:2020-02-25 Published:2020-04-14
Contact: Gongbao LI E-mail:ligb@mail.ccnu.edu.cn
Supported by:
This work was supported by Natural Science Foundation of China (11771166), Hubei Key Laboratory of Mathematical Sciences and Program for Changjiang Scholars and Innovative Research Team in University #IRT_17R46. Niu was financially supported by funding for basic research business in Central Universities (innovative funding projects) (2018CXZZ090).

摘要/Abstract

摘要： In the present paper, we consider the nonlocal Kirchhoff problem
- (ε²a + εb∫_R³ |▽u|²)△u + u = Q(x)u^p, u > 0 in R³,
where a, b > 0, 1 < p < 5 and ε > 0 is a parameter. Under some assumptions on Q(x), we show the existence and local uniqueness of positive multi-peak solutions by LyapunovSchmidt reduction method and the local Pohozaev identity method, respectly.

关键词: Kirchhoff equations, multi-peak positive solutions, local uniqueness, local Pohozaev identity, Lyapunov-Schmidt reduction

Abstract: In the present paper, we consider the nonlocal Kirchhoff problem
- (ε²a + εb∫_R³ |▽u|²)△u + u = Q(x)u^p, u > 0 in R³,
where a, b > 0, 1 < p < 5 and ε > 0 is a parameter. Under some assumptions on Q(x), we show the existence and local uniqueness of positive multi-peak solutions by LyapunovSchmidt reduction method and the local Pohozaev identity method, respectly.

Key words: Kirchhoff equations, multi-peak positive solutions, local uniqueness, local Pohozaev identity, Lyapunov-Schmidt reduction

中图分类号:

35A01

李工宝, 牛亚慧. THE EXISTENCE AND LOCAL UNIQUENESS OF MULTI-PEAK POSITIVE SOLUTIONS TO A CLASS OF KIRCHHOFF EQUATION[J]. 数学物理学报(英文版), 2020, 40(1): 90-112.

Gongbao LI, Yahui NIU. THE EXISTENCE AND LOCAL UNIQUENESS OF MULTI-PEAK POSITIVE SOLUTIONS TO A CLASS OF KIRCHHOFF EQUATION[J]. Acta mathematica scientia,Series B, 2020, 40(1): 90-112.

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THE EXISTENCE AND LOCAL UNIQUENESS OF MULTI-PEAK POSITIVE SOLUTIONS TO A CLASS OF KIRCHHOFF EQUATION

THE EXISTENCE AND LOCAL UNIQUENESS OF MULTI-PEAK POSITIVE SOLUTIONS TO A CLASS OF KIRCHHOFF EQUATION

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