Acta mathematica scientia,Series B ›› 2020, Vol. 40 ›› Issue (1): 90-112.doi: 10.1007/s10473-020-0107-y

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

Gongbao LI, Yahui NIU   

  1. 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).

Abstract: In the present paper, we consider the nonlocal Kirchhoff problem
- (ε2a + εbR3 |▽u|2)△u + u = Q(x)up, 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

CLC Number: 

  • 35A01
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