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On Solvability of a Class of Multidimensional Integral Equations in the Mathematical Theory of Geographic Distribution of an Epidemic

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Abstract

A multidimensional convolution-type integral equations with concave nonlinearity is investigated. This equation arises in the mathematical theory of the geographic distribution of an epidemic. The combination of well-known multidimensional methods and operator methods for constructing invariant cone segments for such operators with methods of the theory of convolution-type integral operators and limit theorems of the function theory allow proving the existence of positive bounded solutions to such equations. The asymptotic behavior of the constructed solutions is also studied. In a specific cone segment, the uniqueness of the solution is also proved. Particular applied examples of these equations are given.

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ACKNOWLDEGMENTS

The authors thank the reviewer for his/her useful remarks.

Funding

The study is supported by the Russian Science Foundation, project no. 19-11-00223.

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Authors and Affiliations

  1. Yerevan State University, Yerevan, Armenia

    Kh. A. Khachatryan

  2. Lomonosov Moscow State University, Moscow, Russia

    Kh. A. Khachatryan & H. S. Petrosyan

  3. Armenian National Agrarian University, Yerevan, Armenia

    H. S. Petrosyan

Authors
  1. Kh. A. Khachatryan
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  2. H. S. Petrosyan
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Corresponding authors

Correspondence to Kh. A. Khachatryan or H. S. Petrosyan.

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Translated by E. Oborin

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Khachatryan, K.A., Petrosyan, H.S. On Solvability of a Class of Multidimensional Integral Equations in the Mathematical Theory of Geographic Distribution of an Epidemic. J. Contemp. Mathemat. Anal. 56, 143–157 (2021). https://doi.org/10.3103/S1068362321030055

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  • DOI: https://doi.org/10.3103/S1068362321030055

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