An ODE reduction method for the semi-Riemannian Yamabe problem on space forms

DOI10.1016/j.na.2021.112342zbMath1483.53059arXiv2008.07041OpenAlexW3145015394WikidataQ115342833 ScholiaQ115342833MaRDI QIDQ2033036

Juan Carlos Fernández, Oscar Palmas

Publication date: 14 June 2021

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2008.07041

zbMATH Keywords

nodal solutionsblowing-up solutionsisoparametric functionsgeneralized Emden-Fowler equationssemi-Riemannian isoparametric hypersurfacessemi-Riemannian Yamabe problem

Mathematics Subject Classification ID

Critical exponents in context of PDEs (35B33) Global submanifolds (53C40) Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics (53C50) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Singular nonlinear boundary value problems for ordinary differential equations (34B16) Hyperbolic equations on manifolds (58J45) Blow-up in context of PDEs (35B44) Entire solutions to PDEs (35B08) Symmetries, invariants, etc. in context of PDEs (35B06) Conformal structures on manifolds (53C18)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Hyperbolic Yamabe problem
• Global well-posedness, scattering and blow-up for the energy-critical focusing non-linear wave equation
• Isoparametrische Hyperflächen in Sphären. I
• On the inequality \(\Delta u \geqq f (u)\)
• Isoparametric hypersurfaces in the pseudo-Riemannian space forms
• Lorentzian isoparametric hypersurfaces in \(H_1^{n+1}\)
• Nonlinear elliptic equations on compact Riemannian manifolds and asymptotics of Emden equations
• Analysis on the minimal representation of O(\(p,\) \(q\)). III: Ultrahyperbolic equations on \(\mathbb{R}^{p-1,q-1}\)
• Isoparametric hypersurfaces with \((g,m)=(6,2)\)
• Supercritical elliptic problems on the round sphere and nodal solutions to the Yamabe problem in projective spaces
• Isoparametric hypersurfaces and metrics of constant scalar curvature
• Isoparametric hypersurfaces with four principal curvatures. IV
• Global bifurcation techniques for Yamabe type equations on Riemannian manifolds
• About the Lorentzian Yamabe problem
• Lorentzian isoparametric hypersurfaces
• Low energy nodal solutions to the Yamabe equation
• Einstein manifolds
• Some properties of the solutions of \([p(t)x''+ q(t)f(x) = 0\)]
• Geometry of Hypersurfaces
• The Yamabe problem
• Recent progress on the Yamabe problem

This page was built for publication: An ODE reduction method for the semi-Riemannian Yamabe problem on space forms