数学物理学报(英文版) ›› 2022, Vol. 42 ›› Issue (5): 2078-2086.doi: 10.1007/s10473-022-0520-2

• 论文 • 上一篇    

GLOBAL STRUCTURE OF A NODAL SOLUTIONS SET OF MEAN CURVATURE EQUATION IN STATIC SPACETIME

Hua LUO1, Guowei DAI2   

  1. 1. School of Economics and Finance, Shanghai International Studies University, Shanghai, 201620, China;
    2. School of Mathematical Sciences, Dalian University of Technology, Dalian, 116024, China
  • 收稿日期:2020-05-22 修回日期:2022-04-24 发布日期:2022-11-02
  • 通讯作者: Guowei Dai,E-mail:daiguowei@dlut.edu.cn E-mail:daiguowei@dlut.edu.cn
  • 基金资助:
    Research supported by NNSF of China (11871129), Xinghai Youqing funds from Dalian University of Technology, NSF of Liaoning Province (2019-MS-109) and HSSF of Chinese Ministry of Education (20YJA790049).

GLOBAL STRUCTURE OF A NODAL SOLUTIONS SET OF MEAN CURVATURE EQUATION IN STATIC SPACETIME

Hua LUO1, Guowei DAI2   

  1. 1. School of Economics and Finance, Shanghai International Studies University, Shanghai, 201620, China;
    2. School of Mathematical Sciences, Dalian University of Technology, Dalian, 116024, China
  • Received:2020-05-22 Revised:2022-04-24 Published:2022-11-02
  • Contact: Guowei Dai,E-mail:daiguowei@dlut.edu.cn E-mail:daiguowei@dlut.edu.cn
  • Supported by:
    Research supported by NNSF of China (11871129), Xinghai Youqing funds from Dalian University of Technology, NSF of Liaoning Province (2019-MS-109) and HSSF of Chinese Ministry of Education (20YJA790049).

摘要: By bifurcation and topological methods, we study the global structure of a radial nodal solutions set of the mean curvature equation in a standard static spacetime \begin{eqnarray} \text{div} \left(\frac{a\nabla u}{\sqrt{1-a^2\vert \nabla u\vert^2}}\right)+\frac{g(\nabla u, \nabla a)}{\sqrt{1-a^2\vert \nabla u\vert^2}}=\lambda NH,\nonumber \end{eqnarray} with a $0$-Dirichlet boundary condition on the unit ball. According to the behavior of $H$ near $0$, we obtain the global structure of sign-changing radial spacelike graphs for this problem.

关键词: bifurcation, static spacetime, mean curvature operator, nodal solution

Abstract: By bifurcation and topological methods, we study the global structure of a radial nodal solutions set of the mean curvature equation in a standard static spacetime \begin{eqnarray} \text{div} \left(\frac{a\nabla u}{\sqrt{1-a^2\vert \nabla u\vert^2}}\right)+\frac{g(\nabla u, \nabla a)}{\sqrt{1-a^2\vert \nabla u\vert^2}}=\lambda NH,\nonumber \end{eqnarray} with a $0$-Dirichlet boundary condition on the unit ball. According to the behavior of $H$ near $0$, we obtain the global structure of sign-changing radial spacelike graphs for this problem.

Key words: bifurcation, static spacetime, mean curvature operator, nodal solution

中图分类号: 

  • 34C23