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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2021, Volume 499, Pages 35–39
DOI: https://doi.org/10.31857/S2686954321040123 (Mi danma186) 		 
This article is cited in 5 scientific papers (total in 5 papers)

MATHEMATICS

Application of special function spaces to the study of nonlinear integral equations arising in equilibrium spatial logistic dynamics

M. V. Nikolaeva, U. Dieckmannbc, A. A. Nikitinad

a Lomonosov Moscow State University, Moscow, Russia
b International Institute for Applied Systems Analysis, Laxenburg, Austria
c Department of Evolutionary Studies of Biosystems, The Graduate University for Advanced Studies (Sokendai), Hayama, Japan
d National Research University "Higher School of Economics", Moscow, Russia
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DOI: https://doi.org/10.31857/S2686954321040123
Abstract: In this paper, we study a nonlinear integral equation that arises in a model of spatial logistic dynamics. The solvability of this equation is investigated by introducing special spaces of functions that are integrable up to a constant. Sufficient conditions for the biological characteristics and the parameters of the third spatial moment closure are established that guarantee the existence of the solution of the equation described above in some ball centered at zero. In addition, it is shown that this solution is unique in the considered ball and not zero. This means that, under appropriate conditions, the equilibrium state of the population of a certain species exists and does not coincide with the state of extinction.
Keywords: functional analysis, nonlinear integral equations, mathematical biology.
Funding agency Grant number
HSE Academic Fund Programme 20-04-021
This work was supported by the Science Foundation of the National Research University Higher School of Economics, project no. 20-04-021.
Presented: I. A. Sokolov
Received: 31.03.2021
Revised: 04.04.2021
Accepted: 07.05.2021
English version:
Doklady Mathematics, 2021, Volume 104, Issue 1, Pages 188–192
DOI: https://doi.org/10.1134/S1064562421040128
Bibliographic databases:
Document Type: Article
UDC: 517.968.43
Language: Russian
Citation: M. V. Nikolaev, U. Dieckmann, A. A. Nikitin, “Application of special function spaces to the study of nonlinear integral equations arising in equilibrium spatial logistic dynamics”, Dokl. RAN. Math. Inf. Proc. Upr., 499 (2021), 35–39; Dokl. Math., 104:1 (2021), 188–192
Citation in format AMSBIB
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