Geodesic
The positive solutions to quasilinear elliptic inequalities on model Riemannian manifolds
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2015), pp. 22-30

Voir la notice de l'article provenant de la source Math-Net.Ru

We investigate the problem of implementation of Liouville type theorems on the existence of positive solutions to some quasilinear elliptic inequalities on model (spherically symmetric) Riemannian manifolds. In particular, we find exact conditions for the existence and nonexistence of entire positive solutions to the studied inequalities on the Riemannian manifolds. The method is based on study of radially symmetric solutions to an ordinary differential equation generated by the basic inequality and establish the relationship of the existence of entire positive solutions to quasilinear elliptic inequalities and solvability of the Cauchy problem for this equation. Moreover, in the paper we apply classical methods of the theory of elliptic equations and inequalities the second order (the maximum principle, the principle of comparison, etc.). The results generalize similar results, obtained previously by Y. Naito and H. Usami for Euclidean space $\mathbf R^n$, as well as some earlier results of the papers by A. G. Losev and E. A. Mazepa.
Keywords: quasilinear elliptic inequalities, entire positive solutions, Liouville type theorems, model Riemannian manifolds.
Mots-clés : conditions of existence 
@article{IVM_2015_9_a2,
     author = {E. A. Mazepa},
     title = {The positive solutions to quasilinear elliptic inequalities on model {Riemannian} manifolds},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {22--30},
     publisher = {mathdoc},
     number = {9},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2015_9_a2/}
}
TY  - JOUR
AU  - E. A. Mazepa
TI  - The positive solutions to quasilinear elliptic inequalities on model Riemannian manifolds
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2015
SP  - 22
EP  - 30
IS  - 9
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2015_9_a2/
LA  - ru
ID  - IVM_2015_9_a2
ER  - 
%0 Journal Article
%A E. A. Mazepa
%T The positive solutions to quasilinear elliptic inequalities on model Riemannian manifolds
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2015
%P 22-30
%N 9
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2015_9_a2/
%G ru
%F IVM_2015_9_a2
E. A. Mazepa. The positive solutions to quasilinear elliptic inequalities on model Riemannian manifolds. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2015), pp. 22-30. http://geodesic.mathdoc.fr/item/IVM_2015_9_a2/