Structure of positive radial solutions of semilinear elliptic equations

We study the positive radial solutions of a semilinear elliptic equation Delta u + f(u) = 0, where f(u) has a supercritical growth order for small u > O and a subcritical growth order for large u. By showing the uniqueness of positive solutions behaving like 0(\x\(2-n)) at infinity, we give an almost complete description for the structure of positive radial solutions. As a consequence, we also prove the uniqueness of positive solutions of the nonlinear Dirichlet problem for the equation in a finite ball. (C) 1997 Academic Press