Release Time:2019-03-12  Hits:

Indexed by: Journal Article

Date of Publication: 2018-06-15

Journal: JOURNAL OF DIFFERENTIAL EQUATIONS

Included Journals: Scopus、SCIE

Volume: 264

Issue: 12

Page Number: 7242-7269

ISSN: 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.