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

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.

References in corpus (4)

• A variational analysis of Einstein-scalar field Lichnerowicz equations on compact Riemannian manifolds
• The constraint equations for the Einstein-scalar field system on compact manifolds
• The Constraint Equations
• Non-CMC Solutions to the Einstein Constraint Equations on Asymptotically Euclidean Manifolds with Apparent Horizon Boundaries