The aim of this paper is to investigate the structure of radial solutions f
or a semilinear elliptic equation Delta u + (y.del u)/2 + u/(p - 1) + \u\(p
-1)u = 0, y epsilon R-n, which is related to forward self-similar solutions
of a semilinear parabolic equation nu(t) = Delta nu + \v\(p-1)nu, (t, x) e
psilon (0,infinity) x R-n. We study the existence, uniqueness, and paramete
r dependency of rapidly decaying solutions with a prescribed number of zero
s. (C) 2000 Academic Press.