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

doi:10.1007/s10473-022-0520-2

Abstract

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

CLC Number:

34C23

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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