Stability and qualitative properties of radial solutions of the Lane–Emden–Fowler equation on Riemannian models

Abstract

We study existence, uniqueness and stability of radial solutions of the Lane–Emden–Fowler equation −Δgu=|u|p−1u in a class of Riemannian models (M,g) of dimension n⩾3 which includes the classical hyperbolic space Hn as well as manifolds with sectional curvatures unbounded below. Sign properties and asymptotic behavior of solutions are influenced by the critical Sobolev exponent while the so-called Joseph–Lundgren exponent is involved in the stability of solutions.