ON THE STRUCTURE OF THE CONFORMAL SCALAR CURVATURE EQUATION ON R(N)

In this paper we wish to conduct a thorough study of the conformal scalar curvature equation ((1.1) below) in R(n), n greater-than-or-equal-to 3, in case the prescribed scalar curvature function K is negative. First, we establish the existence and uniqueness of the maximal positive solution. Then a complete classification of all possible positive solutions is obtained if K behaves like - Absolute value of x(-l) near infinity for some constant l > 2.