CLASSIFICATION OF THE STRUCTURE OF POSITIVE RADIAL SOLUTIONS TO DELTA-U-BAR-X-VERTICAL-BAR) U(P)=0 IN R(N)(K(VERTICAL)

Positive radial solutions to the semilinear elliptic equation Delta u + K(\x\)u(p) = 0 in R(n) are studied, where p > 1, n > 2 and K greater than or equal to 0. It is shown that, under a general condition on K( r) and p, the structure of positive radial solutions becomes one of th ree types. We give sharp criteria to classify the type of the structur e, and apply the result to the conformal scalar curvature equation.