Classification of radial solutions to Hénon type equation on the hyperbolic space

Abstract

We devote this paper to classifying radial solutions of a weighted semilinear elliptic equation on the hyperbolic space. More precisely, for a weighted Lane-Emden equation on the hyperbolic space, we shall study the sign and asymptotic behavior of the radial solutions. We shall also show the existence of fast-decay sign-changing solutions to the Lane-Emden equation on the hyperbolic space.