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Indexed by:期刊论文

Date of Publication:2018-06-15

Journal:JOURNAL OF DIFFERENTIAL EQUATIONS

Included Journals:SCIE、Scopus

Volume:264

Issue:12

Page Number:7242-7269

ISSN No.:0022-0396

Key Words:Bifurcation; Mean curvature spacelike equation; Positive solution; Friedmann-Lemaitre-Robertson-Walker spacetime

Abstract:We study the existence of spacelike graphs for the prescribed mean curvature equation in the Friedmann-Lemaitre-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. (C) 2018 Elsevier Inc. All rights reserved.