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{A formula is presented}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 {less-than or slanted equal to} 0. Then any radial solution u = u ( r ), r = | x |, 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.