Existence results for the Einstein-scalar field Lichnerowicz equations on compact Riemannian manifolds

DOI10.1016/j.aim.2012.04.007zbMath1256.58009OpenAlexW2077089739WikidataQ115362076 ScholiaQ115362076MaRDI QIDQ436155

Xingwang Xu, Quoc-Anh Ngô

Publication date: 30 July 2012

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aim.2012.04.007

zbMATH Keywords

mountain pass theoremPalais-Smale conditioncritical exponentEinstein-scalar field equationLichnerowicz equationnegative exponentPicone type identitysign-changing nonlinearity

Mathematics Subject Classification ID

Einstein's equations (general structure, canonical formalism, Cauchy problems) (83C05) Hyperbolic equations on manifolds (58J45)

Related Items (11)

The general relativistic constraint equations ⋮ The initial-value formulation of the λ-R model ⋮ On properties of positive solutions to nonlinear tri-harmonic and bi-harmonic equations with negative exponents ⋮ Elliptic equation with critical and negative exponents involving the GJMS operator on compact Riemannian manifolds ⋮ The Einstein-scalar field constraint system in the positive case ⋮ On the \(p\)-Laplacian Lichnerowicz equation on compact Riemannian manifolds ⋮ Bifurcating solutions of the Lichnerowicz equation ⋮ Existence results for the Einstein-scalar field Lichnerowicz equations on compact Riemannian manifolds in the null case ⋮ On the Einstein-scalar field Lichnerowicz equations on compact Riemannian manifolds ⋮ Prescribing Webster scalar curvature on CR manifolds of negative conformal invariants ⋮ Effective multiplicity for the Einstein-scalar field Lichnerowicz equation

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