Communications on Pure and Applied Analysis (CPAA)

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

Pages: 871 - 888, Volume 4, Issue 4, December 2005      doi:10.3934/cpaa.2005.4.871

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Hiroshi Morishita - Department of Economics and Information Science, Hyogo University, Kakogawa, 675-0101, Japan (email)
Eiji Yanagida - Mathematical Institute Tohoku University, 6-3Aoba, Aramaki, Aoba-ku, Sendai-shi, 980-8578, Japan (email)
Shoji Yotsutani - Department of Applied Mathematics and Informatics, Ryukoku University, Seta, Otsu, 520-2194, Japan (email)

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

Received: June 2005;      Available Online: September 2005.