Abstract
In this paper, we shall discuss separation phenomena of radial solutions to the Lane-Emden equation on non-compact Riemannian manifolds. In particular, we shall prove the separation property of radial solutions for the supercritical case in the sense of the Joseph-Lundgren, and show that the Joseph-Lundgren exponent is a critical exponent on the separation phenomena of radial solutions. Moreover, we also discuss the stability of radial solutions and the existence of a singular solution.
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