Global bifurcation of solutions of the mean curvature spacelike equation in certain Friedmann-Lemaître-Robertson-Walker spacetimes

DOI10.1016/J.JDE.2018.02.014zbMath1391.35043OpenAlexW2792477328MaRDI QIDQ1708134

Alfonso Romero, Pedro J. Torres, Guowei Dai

Publication date: 4 April 2018

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2018.02.014

zbMATH Keywords

conformal change of variableexistence of spacelike graphs

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics (53C50) Bifurcations in context of PDEs (35B32) Local differential geometry of Lorentz metrics, indefinite metrics (53B30) Positive solutions to PDEs (35B09)

Related Items (9)

Global structure of a nodal solutions set of mean curvature equation in static spacetime ⋮ Infinitely many sign-changing solutions of the Neumann problem in some FLRW spacetimes ⋮ Global bifurcation of positive solutions of a quasilinear indefinite Neumann problem in some FLRW spacetimes ⋮ Spectrum, bifurcation and hypersurfaces of prescribed k-th mean curvature in Minkowski space ⋮ Nonspurious solutions of the Dirichlet problem for the prescribed mean curvature spacelike equation in a Friedmann-Lemaître-Robertson-Walker spacetime ⋮ Unnamed Item ⋮ Lyapunov-type inequalities for one-dimensional Minkowski-curvature problems ⋮ Global bifurcation of solutions of the mean curvature spacelike equation in certain standard static spacetimes ⋮ Some results on surfaces with different mean curvatures in \({\mathbb{R}}^{N+1}\) and \({\mathbb{L}}^{N+1} \)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Prescribed mean curvature graphs with Neumann boundary conditions in some FLRW spacetimes
• Republication of: A homogeneous universe of constant mass and increasing radius accounting for the radial velocity of extra-galactic nebulae
• Bifurcation and positive solutions for problem with mean curvature operator in Minkowski space
• Two Whyburn type topological theorems and its applications to Monge-Ampère equations
• Spacelike hypersurfaces with prescribed boundary values and mean curvature
• Entire spacelike hypersurfaces of constant mean curvature in Minkowski space
• On some nonlinear Sturm-Liouville problems
• Maximal space-like hypersurfaces in the Lorentz-Minkowski spaces
• Periodic solution for nonlinear systems with \(p\)-Laplacian-like operators
• Uniqueness of complete spacelike hypersurfaces of constant mean curvature in generalized Robertson-Walker spacetimes
• Positive radial solutions for Dirichlet problems with mean curvature operators in Minkowski space
• On the curvature of space.
• On the possibility of a world with constant negative curvature of space.
• On bifurcation from infinity
• Multiple positive radial solutions for a Dirichlet problem involving the mean curvature operator in Minkowski space
• Some global results for nonlinear eigenvalue problems
• Existence and multiplicity of entire radial spacelike graphs with prescribed mean curvature function in certain Friedmann–Lemaître–Robertson–Walker spacetimes

This page was built for publication: Global bifurcation of solutions of the mean curvature spacelike equation in certain Friedmann-Lemaître-Robertson-Walker spacetimes