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arXiv · 1307.2416

Effective multiplicity for the Einstein-scalar field Lichnerowicz equation

Bruno Premoselli
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Abstract

We prove the stability of the Einstein-scalar field Lichnerowicz equation under subcritical perturbations of the critical nonlinearity in dimensions 3, 4 and 5. As a consequence, we obtain the existence of a second solution to the equation in several cases. In particular, in the positive case, including the CMC positive cosmological constant case, we show that each time a solution exists, the equation produces a second solution with the exception of one critical value for which the solution is unique.

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Bruno Premoselli. 2013-07-09. Effective multiplicity for the Einstein-scalar field Lichnerowicz equation. https://arxiv.org/abs/1307.2416

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