Global bifurcation of solutions of the mean curvature spacelike equation in certain standard static spacetimes
Metadatos
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AMER INST MATHEMATICAL SCIENCES-AIMS
Materia
Bifurcation Mean curvature operator One-sign solution
Fecha
2020Referencia bibliográfica
Dai, G., Romero, A., & Torres, P. J. Global bifurcation of solutions of the mean curvature spacelike equation in certain standard static spacetimes. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS SERIES S Volume 13, Number 11, November 2020, pp. 3047–3071. [doi: 10.3934/dcdss.2020118]
Patrocinador
National Natural Science Foundation of China (NSFC) 11871129; Xinghai Youqing funds from Dalian University of Technology; Spanish MINECO; European Union (EU) MTM2016-78807-C2-1-P MTM2017-82348-C2-1-PResumen
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.