GLOBAL BIFURCATION OF SOLUTIONS OF THE MEAN CURVATURE SPACELIKE EQUATION IN CERTAIN STANDARD STATIC SPACETIMES

被引：3
|
作者：
Dai, Guowei [1 ]
Romero, Alfonso [2 ]
Torres, Pedro J. [3 ,4 ]
机构：
[1] Dalian Univ Technol, Sch Math Sci, Dalian 116024, Peoples R China
[2] Univ Granada, Dept Geometria & Topol, Granada 18071, Spain
[3] Univ Granada, Dept Matemat Aplicada, Granada 18071, Spain
[4] Univ Granada, Res Unit Modeling Nat MNat, Granada 18071, Spain
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S | 2020年 / 13卷 / 11期
关键词：
Bifurcation; mean curvature operator; one-sign solution; entire spacelike graph; POSITIVE RADIAL SOLUTIONS; DIRICHLET PROBLEM; HYPERSURFACES; OPERATOR;
D O I：
10.3934/dcdss.2020118
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study the existence/nonexistence and multiplicity of spacelike graphs for the following mean curvature equation in a standard static spacetime div (a del u/root 1-a(2)vertical bar del u vertical bar(2)) + g (del u, del a)/root 1-a(2)vertical bar del u vertical bar(2) = lambda NH with 0-Dirichlet boundary condition on the unit ball. According to the behavior of H near 0, we obtain the global structure of one-sign radial spacelike graphs for this problem. Moreover, we also obtain the existence and multiplicity of entire spacelike graphs.
引用
收藏
页码：3047 / 3071
页数：25
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