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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2021, Number 3, Pages 67–75
DOI: https://doi.org/10.26907/0021-3446-2021-3-67-75 (Mi ivm9658) 		 
This article is cited in 1 scientific paper (total in 1 paper)

On capacitary characteristics of noncompact Riemannian manifolds

A. G. Losev, V. V. Filatov

Volgograd state university, 100 University Ave., Volgograd, 400062 Russia
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DOI: https://doi.org/10.26907/0021-3446-2021-3-67-75
Abstract: In this paper we introduce the concept of $L$-massive subsets of non-compact Riemannian manifolds, also their properties are studied. It is proved that non-trivial bounded solution of considered equation exists on non-compact Riemannian manifold if and only if there is $L$-massive set on it. Also proved similar statement for solutions of semilinear equations with finite energy integral.
Keywords: semilinear equation, energy integral, massive sets, Liouville type theorem.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 0633-2020-0003
Received: 23.04.2020
Revised: 23.04.2020
Accepted: 29.06.2020
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2021, Volume 65, Issue 3, Pages 61–67
DOI: https://doi.org/10.3103/S1066369X21030063
Bibliographic databases:
Document Type: Article
UDC: 517
Language: Russian
Citation: A. G. Losev, V. V. Filatov, “On capacitary characteristics of noncompact Riemannian manifolds”, Izv. Vyssh. Uchebn. Zaved. Mat., 2021, no. 3, 67–75; Russian Math. (Iz. VUZ), 65:3 (2021), 61–67
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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