A unified approach to the structure of radial solutions for semilinear elliptic problems

Abstract

Radial solutions of semilinear elliptic problems satisfy some boundary value problems for second order differential equations. It is shown that the boundary value problems can be reduced to a canonical form after suitable change of variables. Through the canonical form, we can study the properties of radial solutions of semilinear elliptic equations in a systematic way, and make clear unknown structure of various equations. We also clarify the implication of the Kelvin transformation and the Rellich-Pohozaev identity, and give their generalized forms.