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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 |
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