Global bifurcation of solutions of the mean curvature spacelike equation in certain Friedmann-Lemaître-Robertson-Walker spacetimes
MetadataShow full item record
Guowei, D., Romero Sarabia, A., Torres Villarroya, P.J.. Differential Equations vol. 264, no. 12, pp. 7242–7269, 2018.
We study the existence of spacelike graphs for the prescribed mean curvature equation in the Friedmann-Lemaˆıtre-Robertson-Walker (FLRW) spacetime. By using a conformal change of variable, this problem is translated into an equivalent problem in the Lorentz-Minkowski spacetime. Then, by using Rabinowitz’s global bifurcation method, we obtain the existence and multiplicity of positive solutions for this equation with 0-Dirichlet boundary condition on a ball. Moreover, the global structure of the positive solution set is studied