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

Y. Kabeya; Eiji Yanagida; Shoji Yotsutani

doi:10.3934/cpaa.2002.1.85

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2002, Volume 1, Issue 1: 85-102. Doi: 10.3934/cpaa.2002.1.85

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

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

Received: August 31, 2001

Published: February 2002

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Abstract

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.

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Mathematics Subject Classification: 35J25, 34B16.

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