On asymptotic behavior of positive solutions of some quasilinear inequalities on model Riemannian manifolds

Abstract

In the paper we study asymptotic behavior of positive solutions to some quasilinear elliptic inequalities on spherically symmetric noncompact (model) Riemannian manifolds. In particular, we find conditions under which Liouville type theorems on absence of nontrivial solutions hold true, as well as the conditions of existence and cardinality of the set of positive solutions of the studied inequalities on the Riemannian manifolds. The results generalize similar results obtained previously by Y. Naito and H. Usami for the Euclidean space $\mathbf{R}^n $.