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

• 论文 • 上一篇    下一篇

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. 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. 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: 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