Structure of positive radial solutions including singular solutions to Matukuma's equation

Hiroshi Morishita; Eiji Yanagida; Shoji Yotsutani

doi:10.3934/cpaa.2005.4.871

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2005, Volume 4, Issue 4: 871-888. Doi: 10.3934/cpaa.2005.4.871

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Structure of positive radial solutions including singular solutions to Matukuma's equation

1.
Department of Economics and Information Science, Hyogo University, Kakogawa, 675-0101
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: June 2005

Published: December 2005

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Abstract

We consider positive solutions of Matukuma's equation, which is described by a nonlinear elliptic equation with a weight. Any radially symmetric solution of this equation is said to be regular or singular according to its behavior near the origin and infinity. We investigate the structure of positive radial regular and singular solutions.

Keywords:

Semilinear elliptic equation,
radial solutions.

Mathematics Subject Classification: 35J25, 34B16.

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