Alternating bounded solutions of a class of nonlinear two-dimensional convolution-type integral equations

Khachatryan, Kh.; Petrosyan, A.

doi:10.1090/mosc/329

Alternating bounded solutions of a class of nonlinear two-dimensional convolution-type integral equations
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by Kh. A. Khachatryan and A. S. Petrosyan
Translated by: Nadezhda Andreevna Berestova

Trans. Moscow Math. Soc. 2021, 259-271

DOI: https://doi.org/10.1090/mosc/329

Published electronically: March 15, 2022

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Abstract:

This paper is devoted to studying a class of nonlinear two-dimensional convolution-type integral equations on $\mathbb {R}^2$. This class of equations has applications in the theory of $p$-adic open-closed strings and in the mathematical theory of the spread of epidemics in space and time. The existence of an alternating bounded solution is proved. The asymptotic behaviour of the constructed solution is also studied in a particular case. At the end of the paper, specific applied examples of these equations are given to illustrate the results. UDK 517.968.4.

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