E. Yanagida et S. Yotsutani, CLASSIFICATION OF THE STRUCTURE OF POSITIVE RADIAL SOLUTIONS TO DELTA-U-BAR-X-VERTICAL-BAR) U(P)=0 IN R(N)(K(VERTICAL), Archive for Rational Mechanics and Analysis, 124(3), 1993, pp. 239-259
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.