Please use this identifier to cite or link to this item: https://doi.org/10.1016/j.aim.2012.04.007
Title: Existence results for the Einstein-scalar field Lichnerowicz equations on compact Riemannian manifolds
Authors: Ngô, Q.A.
Xu, X. 
Keywords: Critical exponent
Einstein-scalar field equation
Lichnerowicz equation
Mountain pass theorem
Negative exponent
Palais-Smale condition
Picone type identity
Sign-changing nonlinearity
Issue Date: Jul-2012
Citation: Ngô, Q.A., Xu, X. (2012-07). Existence results for the Einstein-scalar field Lichnerowicz equations on compact Riemannian manifolds. Advances in Mathematics 230 (4-6) : 2378-2415. ScholarBank@NUS Repository. https://doi.org/10.1016/j.aim.2012.04.007
Abstract: This article mainly concerns with the non-existence, existence, and multiplicity results for positive solutions to the Einstein-scalar field Lichnerowicz equation on closed manifolds with a negative conformal-scalar field invariant. This equation arises from the Hamiltonian constraint equation for the Einstein-scalar field system in general relativity. Our analysis introduces variational techniques to the analysis of the Hamiltonian constraint equation, especially those cases when the prescribed scalar curvature-scalar field function may change sign. To our knowledge, such a problem remains open. © 2012 Elsevier Ltd.
Source Title: Advances in Mathematics
URI: http://scholarbank.nus.edu.sg/handle/10635/103242
ISSN: 00018708
DOI: 10.1016/j.aim.2012.04.007
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