Kurmakaev R.F., Losev A.G. On the asymptotic behaviour unbounded solutions of the elliptic equation on the model riemannian manifolds

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Kurmakaev Ruslan Fedorovich
 
Master Student in “Mathematics”, Volgograd State University
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Prospect Universitetsky, 100, 400062 Volgograd, Russian Federation
 
Losev Alexander Georgievich
 
Doctor of Physics and Mathematics, Professor, Chair of Mathematical Analysis and Function Theory, Dean of Mathematics and Information Technologies Department, Volgograd State University
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Prospect Universitetsky, 100, 400062 Volgograd, Russian Federation

Abstract. In this paper we consider solutions of the some elliptic equations on the noncompact Riemannian manifolds which is the generalized spherically symmetric manifolds. By the spectral properties of such manifolds the exact estimations of the dimension of the space of unbounded solutions of the elliptic equations were obtained.

Key words: Liouville type theorem, model Riemannian manifolds, unbounded Lharmonic functions, potential theory, spectral properties.

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On the asymptotic behaviour unbounded solutions of the elliptic equation on the model Riemannian manifolds by Kurmakaev R.F., Losev A.G. is licensed under a Creative Commons Attribution 4.0 International License.

Citation in English: Science Journal of Volgograd State University. Mathematics. Physics. №2 (17) 2012 pp. 30-40

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