|
Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2015, Number 9, Pages 22–30
(Mi ivm9032)
|
|
|
|
This article is cited in 3 scientific papers (total in 3 papers)
The positive solutions to quasilinear elliptic inequalities on model Riemannian manifolds
E. A. Mazepa Chair of Mathematical Analysis and Function Theory, Volgograd State University, 100 Universitetskii Ave., Volgograd, 400062 Russia
Abstract:
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, conditions of existence, model Riemannian manifolds.
Received: 26.02.2014
Citation:
E. A. Mazepa, “The positive solutions to quasilinear elliptic inequalities on model Riemannian manifolds”, Izv. Vyssh. Uchebn. Zaved. Mat., 2015, no. 9, 22–30; Russian Math. (Iz. VUZ), 59:9 (2015), 18–25
Linking options:
https://www.mathnet.ru/eng/ivm9032 https://www.mathnet.ru/eng/ivm/y2015/i9/p22
|
Statistics & downloads: |
Abstract page: | 170 | Full-text PDF : | 32 | References: | 36 | First page: | 8 |
|