MULTIPLE SOLUTIONS OF SOME ELLIPTIC SYSTEMS WITH LINEAR COUPLINGS

doi:10.1007/s10473-021-0408-6

数学物理学报(英文版) ›› 2021, Vol. 41 ›› Issue (4): 1141-1150.doi: 10.1007/s10473-021-0408-6

MULTIPLE SOLUTIONS OF SOME ELLIPTIC SYSTEMS WITH LINEAR COUPLINGS

陈宇彤¹, 苏加宝¹, 孙明正², 田如顺³

1. School of Mathematical Sciences, Capital Normal University, Beijing 100048, China;
2. College of Sciences, North China University of Technology, Beijing 100144, China;
3. School of Mathematical Sciences, Capital Normal University, Beijing 100048, China

收稿日期:2020-01-29 修回日期:2020-10-30 出版日期:2021-08-25 发布日期:2021-09-01
通讯作者: Rushun TIAN E-mail:rushun.tian@cnu.edu.cn
作者简介:Yutong CHEN,E-mail:chenyutong@cnu.edu.cn;Jiabao SU,E-mail:sujb@cnu.edu.cn;Mingzheng SUN,E-mail:suncut@163.com;Rushun TIAN,E-mail:rushun.tian@cnu.edu.cn
基金资助:
Supported by KZ202010028048, NSFC (12001382, 11771302, 11601353) and Beijing Education Committee (KM201710009012, 6943).

MULTIPLE SOLUTIONS OF SOME ELLIPTIC SYSTEMS WITH LINEAR COUPLINGS

Yutong CHEN¹, Jiabao SU¹, Mingzheng SUN², Rushun TIAN³

1. School of Mathematical Sciences, Capital Normal University, Beijing 100048, China;
2. College of Sciences, North China University of Technology, Beijing 100144, China;
3. School of Mathematical Sciences, Capital Normal University, Beijing 100048, China

Received:2020-01-29 Revised:2020-10-30 Online:2021-08-25 Published:2021-09-01
Contact: Rushun TIAN E-mail:rushun.tian@cnu.edu.cn
Supported by:
Supported by KZ202010028048, NSFC (12001382, 11771302, 11601353) and Beijing Education Committee (KM201710009012, 6943).

摘要/Abstract

摘要： In this paper, we study the existence of nontrivial solutions to the elliptic system \begin{equation*} \begin{cases} -\Delta u=\lambda v + F_u(x,u,v),& \ x\in\Omega,\\ -\Delta v=\lambda u + F_v(x,u,v),& \ x\in\Omega,\\ u=v=0,& \ x\in\partial\Omega, \end{cases} \end{equation*} where $\Omega\subset\mathbb{R}^N$ is bounded with a smooth boundary. By the Morse theory and the Gromoll-Meyer pair, we obtain multiple nontrivial vector solutions to this system.

关键词: Morse theory, multiplicity, elliptic system, linear couplings

Abstract: In this paper, we study the existence of nontrivial solutions to the elliptic system \begin{equation*} \begin{cases} -\Delta u=\lambda v + F_u(x,u,v),& \ x\in\Omega,\\ -\Delta v=\lambda u + F_v(x,u,v),& \ x\in\Omega,\\ u=v=0,& \ x\in\partial\Omega, \end{cases} \end{equation*} where $\Omega\subset\mathbb{R}^N$ is bounded with a smooth boundary. By the Morse theory and the Gromoll-Meyer pair, we obtain multiple nontrivial vector solutions to this system.

Key words: Morse theory, multiplicity, elliptic system, linear couplings

中图分类号:

37B30

陈宇彤, 苏加宝, 孙明正, 田如顺. MULTIPLE SOLUTIONS OF SOME ELLIPTIC SYSTEMS WITH LINEAR COUPLINGS[J]. 数学物理学报(英文版), 2021, 41(4): 1141-1150.

Yutong CHEN, Jiabao SU, Mingzheng SUN, Rushun TIAN. MULTIPLE SOLUTIONS OF SOME ELLIPTIC SYSTEMS WITH LINEAR COUPLINGS[J]. Acta mathematica scientia,Series B, 2021, 41(4): 1141-1150.

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MULTIPLE SOLUTIONS OF SOME ELLIPTIC SYSTEMS WITH LINEAR COUPLINGS

MULTIPLE SOLUTIONS OF SOME ELLIPTIC SYSTEMS WITH LINEAR COUPLINGS

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