Structure of the sets of regular and singular radial solutions for a semilinear elliptic equation

This paper is concerned with the structure of the set of radially symmetric solutions for the equation with n>2. Here the nonlinear term f is assumed to be a smooth function of u that is positive for u>0 and is equal to 0 for u 0. Then any radial solution , of the equation is shown to be classified into one of several types according to its behavior as r→0 and r→∞. Under the assumption that f is supercritical for small u>0 and is subcritical for large u>0, we clarify the entire structure of the set of solutions of various types. The Pohozaev identity plays a crucial role in the investigation of the structure.