Structure of positive radial solutions of Matukuma's equation
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We study the structure of solutions of a semilinear elliptic equation called Matukuma's equation. This equation is a mathematical model for describing the dynamics of a globular cluster of stars. It is known that, under some conditions, there exists a solution called a positive entire solution with finite total mass. It is conjectured that the finite total mass solution is unique. In this paper the structure of positive radial solutions is made clear and an affirmative answer is given to the conjecture.
Key wordssemilinear elliptic equation uniqueness
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- T. Matukuma, The Cosmos. Iwanami Shoten, Tokyo, 1938 (In Japanese).Google Scholar