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

doi:10.1007/s10473-022-0520-2

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. 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. 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/Abstract

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

Hua LUO, Guowei DAI. GLOBAL STRUCTURE OF A NODAL SOLUTIONS SET OF MEAN CURVATURE EQUATION IN STATIC SPACETIME[J]. 数学物理学报(英文版), 2022, 42(5): 2078-2086.

Hua LUO, Guowei DAI. GLOBAL STRUCTURE OF A NODAL SOLUTIONS SET OF MEAN CURVATURE EQUATION IN STATIC SPACETIME[J]. Acta mathematica scientia,Series B, 2022, 42(5): 2078-2086.

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

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

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