# American Institute of Mathematical Sciences

March  2002, 1(1): 85-102. doi: 10.3934/cpaa.2002.1.85

## Canonical forms and structure theorems for radial solutions to semi-linear elliptic problems

 1 Department of Applied Mathematics, Miyazaki University, Kibana, Miyazaki, 889-2192, Japan 2 Mathematical Institute Tohoku University, 6-3Aoba, Aramaki, Aoba-ku, Sendai-shi, 980-8578, Japan 3 Department of Applied Mathematics and Informatics, Ryukoku University, Seta, Otsu, 520-2194, Japan

Received  September 2001 Published  December 2001

We propose a method to investigate the structure of positive radial solutions to semilinear elliptic problems with various boundary conditions. It is already shown that the boundary value problems can be reduced to a canonical form by a suitable change of variables. We show structure theorems to canonical forms to equations with power nonlinearities and various boundary conditions. By using these theorems, it is possible to study the properties of radial solutions of semilinear elliptic equations in a systematic way, and make clear unknown structure of various equations.
Citation: Y. Kabeya, Eiji Yanagida, Shoji Yotsutani. Canonical forms and structure theorems for radial solutions to semi-linear elliptic problems. Communications on Pure & Applied Analysis, 2002, 1 (1) : 85-102. doi: 10.3934/cpaa.2002.1.85
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