SIGN-CHANGING SOLUTIONS FOR THE STATIONARY KIRCHHOFF PROBLEMS INVOLVING THE FRACTIONAL LAPLACIAN IN RN

数学物理学报(英文版) ›› 2018, Vol. 38 ›› Issue (6): 1712-1730.

SIGN-CHANGING SOLUTIONS FOR THE STATIONARY KIRCHHOFF PROBLEMS INVOLVING THE FRACTIONAL LAPLACIAN IN R^N

程琨¹, 高琦²

1 Department of Information Engineering, Jingdezhen Ceramic Institute, Jingdezhen 333403, China;
2 Department of Mathematics, School of Science, Wuhan University of Technology, Wuhan 430070, China

收稿日期:2017-08-09 修回日期:2018-01-11 出版日期:2018-12-25 发布日期:2018-12-28
通讯作者: Qi GAO E-mail:gaoq@whut.edu.cn
作者简介:Kun CHENG,E-mail:chengkun0010@126.com
基金资助:
The second author was supported by the NSFC (11501231), and the "Fundamental Research Funds for the Central Universities" (WUT2017IVA077, 2018IB014).

SIGN-CHANGING SOLUTIONS FOR THE STATIONARY KIRCHHOFF PROBLEMS INVOLVING THE FRACTIONAL LAPLACIAN IN R^N

Kun CHENG¹, Qi GAO²

1 Department of Information Engineering, Jingdezhen Ceramic Institute, Jingdezhen 333403, China;
2 Department of Mathematics, School of Science, Wuhan University of Technology, Wuhan 430070, China

Received:2017-08-09 Revised:2018-01-11 Online:2018-12-25 Published:2018-12-28
Contact: Qi GAO E-mail:gaoq@whut.edu.cn
Supported by:
The second author was supported by the NSFC (11501231), and the "Fundamental Research Funds for the Central Universities" (WUT2017IVA077, 2018IB014).

摘要/Abstract

摘要： In this paper, we study the existence of least energy sign-changing solutions for a Kirchhoff-type problem involving the fractional Laplacian operator. By using the constraint variation method and quantitative deformation lemma, we obtain a least energy nodal solution u_b for the given problem. Moreover, we show that the energy of u_b is strictly larger than twice the ground state energy. We also give a convergence property of u_b as b↘ 0, where b is regarded as a positive parameter.

关键词: Kirchhoff equation, fractional Laplacian, sign-changing solutions

Abstract: In this paper, we study the existence of least energy sign-changing solutions for a Kirchhoff-type problem involving the fractional Laplacian operator. By using the constraint variation method and quantitative deformation lemma, we obtain a least energy nodal solution u_b for the given problem. Moreover, we show that the energy of u_b is strictly larger than twice the ground state energy. We also give a convergence property of u_b as b↘ 0, where b is regarded as a positive parameter.

Key words: Kirchhoff equation, fractional Laplacian, sign-changing solutions

程琨, 高琦. SIGN-CHANGING SOLUTIONS FOR THE STATIONARY KIRCHHOFF PROBLEMS INVOLVING THE FRACTIONAL LAPLACIAN IN R^N[J]. 数学物理学报(英文版), 2018, 38(6): 1712-1730.

Kun CHENG, Qi GAO. SIGN-CHANGING SOLUTIONS FOR THE STATIONARY KIRCHHOFF PROBLEMS INVOLVING THE FRACTIONAL LAPLACIAN IN R^N[J]. Acta mathematica scientia,Series B, 2018, 38(6): 1712-1730.

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SIGN-CHANGING SOLUTIONS FOR THE STATIONARY KIRCHHOFF PROBLEMS INVOLVING THE FRACTIONAL LAPLACIAN IN R^N

SIGN-CHANGING SOLUTIONS FOR THE STATIONARY KIRCHHOFF PROBLEMS INVOLVING THE FRACTIONAL LAPLACIAN IN R^N

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