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Application of a Generalized Fixed Point Principle to the Study of a System of Nonlinear Integral Equations Arising in the Population Dynamics Model

  • INTEGRAL AND INTEGRO-DIFFERENTIAL EQUATIONS
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Abstract

The paper deals with the analysis of a system of nonlinear integral equations resulting from the three-parameter closure of the third spatial moment in the Dieckmann–Law model in the case of an \(n \)-species community in an \(N \)-dimensional space. For the analysis of its solvability, this system is represented as an operator equation in a Banach space of a special form. Sufficient conditions for the existence of a nontrivial solution are stated using a generalized fixed point principle.

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REFERENCES

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Funding

The results in Secs. 1 and 2 of the present paper were obtained by A.A. Nikitin with the financial support of the Russian Science Foundation, project no. 22-11-00042. The remaining results were obtained by all authors with the support of the Ministry of Science and Higher Education of the Russian Federation as part of the implementation of the program of the Moscow Center for Fundamental and Applied Mathematics under agreement no. 075-15-2022-284.

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Authors and Affiliations

  1. Lomonosov Moscow State University, Moscow, 119991, Russia

    M. V. Nikolaev & A. A. Nikitin

  2. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, 117997, Russia

    A. A. Nikitin

  3. Okinawa Institute of Science and Technology Graduate University, Okinawa, 904-0495, Japan

    U. Dieckmann

  4. International Institute for Applied Systems Analysis, Laxenburg, A-2361, Austria

    U. Dieckmann

  5. The Graduate University for Advanced Studies, Hayama, Kanagawa, 240-0193, Japan

    U. Dieckmann

Authors
  1. M. V. Nikolaev
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  2. A. A. Nikitin
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  3. U. Dieckmann
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Corresponding authors

Correspondence to M. V. Nikolaev, A. A. Nikitin or U. Dieckmann.

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Translated by V. Potapchouck

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Nikolaev, M.V., Nikitin, A.A. & Dieckmann, U. Application of a Generalized Fixed Point Principle to the Study of a System of Nonlinear Integral Equations Arising in the Population Dynamics Model. Diff Equat 58, 1233–1241 (2022). https://doi.org/10.1134/S0012266122090087

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  • DOI: https://doi.org/10.1134/S0012266122090087

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