Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

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Petrosyan H. S., Andriyan S. M., Khachatryan K. A. Questions of existence and uniqueness of the solution of one class of an infinite system of nonlinear two-dimensional equations. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2024, vol. 24, iss. 4, pp. 498-511. DOI: 10.18500/1816-9791-2024-24-4-498-511, EDN: HKTFOQ

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
25.11.2024
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Language: 
Russian
Heading: 
Mathematics
Article type: 
Article
UDC: 
517.988.63
DOI: 
10.18500/1816-9791-2024-24-4-498-511
EDN: 
HKTFOQ

Questions of existence and uniqueness of the solution of one class of an infinite system of nonlinear two-dimensional equations

Autors: 
Petrosyan Haykanush S., Armenian National Agrarian University
Andriyan Silva M., Armenian National Agrarian University
Khachatryan Khachatur Agavardovich, Yerevan State University
Abstract: 

The paper is devoted to the study of one class of infinite systems of nonlinear two-dimensional equations with convex and monotone nonlinearity. The studied  class of nonlinear systems of algebraic equations has both theoretical and practical significance, in particular, in the study of discrete analogs of problems in dynamic theory of $p$-adic open-closed strings, in the kinetic theory of gases, in mathematical biology in the study of space-time distribution of epidemics. Existence and uniqueness theorems for a positive solution in a certain class of non-negative and bounded matrices are proved. Some qualitative properties of the solution are revealed. The obtained results supplement and generalize some of the previously obtained ones. Illustrative examples of the corresponding matrices and nonlinearities (including those of an applied nature) that satisfy all the conditions of the formulated theorems are given.

Key words: 
infinite matrix
nonlinearity
convexity
successive approximations
monotonicity
uniqueness
Acknowledgments: 
The work of the third author was supported by the Science Committee of the Republic of Armenian (project No. 23RL-1A027).
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Received: 
20.04.2023
Accepted: 
03.07.2023
Published: 
29.11.2024
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