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On Solutions of a System of Nonlinear Integral Equations of Convolution Type on the Entire Real Line

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Abstract

We consider a special system of integral equations of convolution type with a monotone convex nonlinearity naturally arising when searching for stationary or limit states in various dynamic models of applied nature, for example, in models of the spread of epidemics, and prove theorems stating the existence or absence of a nontrivial bounded solution with limits at \(\pm \infty \) depending on the values of these limits and on the structure of the matrix kernel of the system. We also study the uniqueness of such a solution assuming that it exists. Specific examples of systems whose parameters satisfy the conditions stated in our theorems are given.

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Funding

This work was financially supported by the Russian Science Foundation, project 19-11-00223, https://rscf.ru/en/project/19-11-00223/.

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Authors and Affiliations

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

    A. A. Davydov

  2. Yerevan State University, Yerevan, 0025, Armenia

    Kh. A. Khachatryan

  3. Armenian National Agrarian University, Yerevan, 0009, Armenia

    H. S. Petrosyan

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

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

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Translated by V. Potapchouck

CONFLICT OF INTEREST. The authors of this work declare that they have no conflicts of interest.

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Davydov, A.A., Khachatryan, K.A. & Petrosyan, H.S. On Solutions of a System of Nonlinear Integral Equations of Convolution Type on the Entire Real Line. Diff Equat 59, 1504–1519 (2023). https://doi.org/10.1134/S00122661230110058

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  • DOI: https://doi.org/10.1134/S00122661230110058

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