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

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
Appears in Collections:	Staff Publications

There are no files associated with this item.

Check