Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4666332 | Advances in Mathematics | 2012 | 38 Pages |
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.
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Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Quô´c Anh Ngô, Xingwang Xu,