Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 45, 2020, 121-137

LOCAL UNIQUENESS OF MULTI-PEAK SOLUTIONS TO A CLASS OF KIRCHHOFF EQUATIONS

Gongbao Li, Yahui Niu and Chang-Lin Xiang

Central China Normal University, School of Mathematics and Statistics
Wuhan, 430079, P.R. China; ligb 'at' ail.ccnu.edu.cn

Central China Normal University, School of Mathematics and Statistics
Wuhan, 430079, P.R. China; yahuniu 'at' 163.com

Yangtze University, School of Information and Mathematics
Jingzhou 434023, P.R. China; changlin.xiang 'at' yangtzeu.edu.cn

Abstract. In this paper, we consider the nonlocal Kirchhoff problem

-(ε²a + εb∫_R3 |∇u|²)Δu + V(x)u = u^p, u > 0, u∈ H¹(R³)

where a,b > 0, 1 < p < 5 are constants, ε > 0 is a parameter. Under some assumptions on V(x), we show the local uniqueness of positive multi-peak solutions by using the local Pohozaev identity.

2010 Mathematics Subject Classification: Primary 35A01, 35B25, 35J20, 35J60.

Key words: Kirchhoff equations, multi-peak positive solutions, local uniqueness, local Pohozaev identity.

Reference to this article: G. Li, Y. Niu and C.-L. Xiang: Local uniqueness of multi-peak solutions to a class of Kirchhoff equations. Ann. Acad. Sci. Fenn. Math. 45 (2020), 121-137.

Full document as PDF file

https://doi.org/10.5186/aasfm.2020.4503