The positive solutions to quasilinear elliptic inequalities on model Riemannian manifolds
| العنوان: | The positive solutions to quasilinear elliptic inequalities on model Riemannian manifolds |
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| المؤلفون: | E. A. Mazepa |
| المصدر: | Russian Mathematics. 59:18-25 |
| بيانات النشر: | Allerton Press, 2015. |
| سنة النشر: | 2015 |
| مصطلحات موضوعية: | Pure mathematics, Maximum principle, Euclidean space, General Mathematics, Ordinary differential equation, Ricci-flat manifold, Mathematical analysis, Order (group theory), Initial value problem, Type (model theory), Mathematics |
| الوصف: | We investigate the problem of implementation of the Liouville type theorems on the existence of positive solutions of 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 of the studied inequalities on the Riemannian manifolds. The method is based on a study of radially symmetric solutions of an ordinary differential equation generated by the basic inequality and establishing the relationship of the existence of entire positive solutions of quasilinear elliptic inequalities and solvability of the Cauchy problem for this equation. In addition, in the paper we apply classical methods of the theory of elliptic equations and second order inequalities (the maximum principle, the principle of comparison, etc.). The obtained results generalize similar results obtained previously by Y. Naito and H. Usami for Euclidean space Rn, as well as some earlier results by A. G. Losev and E. A. Mazepa. |
| تدمد: | 1934-810X 1066-369X |
| DOI: | 10.3103/s1066369x15090030 |
| URL الوصول: | https://explore.openaire.eu/search/publication?articleId=doi_________::f48c78d35428462b4124d540bd2f71ca https://doi.org/10.3103/s1066369x15090030 |
| Rights: | CLOSED |
| رقم الانضمام: | edsair.doi...........f48c78d35428462b4124d540bd2f71ca |
| قاعدة البيانات: | OpenAIRE |
| تدمد: | 1934810X 1066369X |
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| DOI: | 10.3103/s1066369x15090030 |