Global bifurcation of solutions of the mean curvature spacelike equation in certain standard static spacetimes

Abstract

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.