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arXiv · 1708.04602

Lichnerowicz-type equations with sign-changing nonlinearities on complete manifolds with boundary

Guglielmo Albanese·Marco Rigoli
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Abstract

We prove an existence theorem for positive solutions to Lichnerowicz-type equations on complete manifolds with boundary and nonlinear Neumann conditions. This kind of nonlinear problems arise quite naturally in the study of solutions for the Einstein-scalar field equations of General Relativity in the framework of the so called Conformal Method.

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Guglielmo Albanese, Marco Rigoli. 2017-08-15. Lichnerowicz-type equations with sign-changing nonlinearities on complete manifolds with boundary. https://doi.org/10.1016/j.jde.2017.08.010

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