We prove an existence theorem for positive solutions to Lichnerowicz-type equations on complete manifolds with boundary (M,∂M,〈,〉) 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.
Lichnerowicz-type equations with sign-changing nonlinearities on complete manifolds with boundary / G. Albanese, M. Rigoli. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - 263:11(2017), pp. 7475-7495. [10.1016/j.jde.2017.08.010]
Lichnerowicz-type equations with sign-changing nonlinearities on complete manifolds with boundary
G. Albanese;M. Rigoli
2017
Abstract
We prove an existence theorem for positive solutions to Lichnerowicz-type equations on complete manifolds with boundary (M,∂M,〈,〉) 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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