论全实线上卷积型非线性积分方程组的解

IF 0.8 4区数学 Q2 MATHEMATICS

Differential Equations Pub Date : 2023-12-29 DOI:10.1134/s00122661230110058

A. A. Davydov, Kh. A. Khachatryan, H. S. Petrosyan

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引用次数: 0

摘要

摘要我们考虑了卷积型积分方程的一个特殊系统，该系统具有单凸非线性，在寻找应用性质的各种动态模型（例如流行病传播模型）中的静止或极限状态时自然会出现，我们证明了这样一个定理，即是否存在一个非孤立的有界解，其极限为（\pm \infty \），取决于这些极限的值和系统矩阵核的结构。我们还研究了假设存在的这种解的唯一性。我们给出了参数满足我们定理所述条件的系统的具体例子。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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

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

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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来源期刊

Differential Equations 数学-数学

CiteScore

1.30

自引率

33.30%

发文量

审稿时长

3-8 weeks

期刊介绍： Differential Equations is a journal devoted to differential equations and the associated integral equations. The journal publishes original articles by authors from all countries and accepts manuscripts in English and Russian. The topics of the journal cover ordinary differential equations, partial differential equations, spectral theory of differential operators, integral and integral–differential equations, difference equations and their applications in control theory, mathematical modeling, shell theory, informatics, and oscillation theory. The journal is published in collaboration with the Department of Mathematics and the Division of Nanotechnologies and Information Technologies of the Russian Academy of Sciences and the Institute of Mathematics of the National Academy of Sciences of Belarus.