Title  Existence results for the Einsteinscalar field Lichnerowicz equations on compact Riemannian manifolds in the positive case 
Publication Type  Journal Article 
Year of Publication  2014 
Authors  Ngô, QAnh, Xu, X 
Journal  Bulletin of the Institute of Mathematics Academia Sinica (New Series) 
Volume  9 
Pagination  451–485 
ISSN  23047909 
Abstract  This is the third and last in our series of papers concerning solution of the Einsteinscalar field Lichnerowicz equations on Riemannian manifolds. Let $(M,g)$ be a smooth compact Riemannian manifold without the boundary of dimension $n \geqslant 3$, $f$, $h>0$, and $a \geqslant 0$ are smooth functions on $M$ with $\int_M a dv_g>0$. In this article, we prove two major results involving the following partial differential equation arising from the Hamiltonian constraint equation for the Einsteinscalar field system in general relativity

URL  http://w3.math.sinica.edu.tw/bulletin/bulletin_id_a.jsp?bid=MjAxNDMwNw== 