Lichnerowicz-type equations with sign-changing nonlinearities on complete manifolds with boundary
Analysis of PDEs
2017-08-16 v1 General Relativity and Quantum Cosmology
Differential Geometry
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.
Keywords
Cite
@article{arxiv.1708.04602,
title = {Lichnerowicz-type equations with sign-changing nonlinearities on complete manifolds with boundary},
author = {Guglielmo Albanese and Marco Rigoli},
journal= {arXiv preprint arXiv:1708.04602},
year = {2017}
}