Abstract
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.
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Y. Li and W.-M. Ni, On conformal scalar curvature equations inR n. Duke Math. J.,57 (1988), 895–924.
Y. Li and W.-M. Ni, On the existence and symmetry properties of finite total mass solutions of Matukuma equation, Eddington equation and their generalizations. Arch. Rational Mech. Anal.,108 (1989), 175–194.
T. Matukuma, The Cosmos. Iwanami Shoten, Tokyo, 1938 (In Japanese).
W.-M. Ni and S. Yotsutani, Semilinear elliptic equations of Matukuma-type and related topics. Japan J. Appl. Math.,5 (1988), 1–32.
E. S. Noussair and C. A. Swanson, Solutions of Matukuma's equation with finite total mass. Indiana Univ. Math. J.,38 (1989), 577–561.
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Yanagida, E. Structure of positive radial solutions of Matukuma's equation. Japan J. Indust. Appl. Math. 8, 165–173 (1991). https://doi.org/10.1007/BF03167191
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DOI: https://doi.org/10.1007/BF03167191