On asymptotical behavior of the solutions some semilinear elliptical equations on noncompact Riemannian manifolds

This paper is devoted to studying the asymptotical behavior of the solutions of some semilinear equations on noncompact Riemannian manifolds. We establish some interrelation between validity of the Liouville property for linear elliptical equations with constant positive potential and validity of the Liouville theorem for one semilinear elliptic equation on these manifolds. Also we receive the necessary and sufficient conditions of existence of the nontrivial (positive) bounded entire solutions of the semilinear elliptic equations and solvability of some boundary value problems on the quasi-model Riemannian manifolds.