Solvability of Some Systems of Integro-differential Equations in Population Dynamics Depending on the Natality and Mortality Rates

Q3 Mathematics Arnold Mathematical Journal Pub Date : 2023-01-27 DOI:10.1007/s40598-023-00225-6

Vitali Vougalter, Vitaly Volpert

引用次数: 0

Abstract

We establish the existence of stationary solutions for certain systems of reaction–diffusion-type equations in the corresponding \(H^{2}\) spaces. Our method relies on the fixed point theorem when the elliptic problem contains second-order differential operators with and without the Fredholm property, which may depend on the outcome of the competition between the natality and the mortality rates involved in the equations of the systems.

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基于出生率和死亡率的人口动力学中某些积分微分方程组的可解性

我们在相应的 \(H^{2}\) 空间中建立了某些反应扩散型方程系统的静态解的存在性。当椭圆问题包含具有或不具有弗雷德霍姆性质的二阶微分算子时，我们的方法依赖于定点定理，而弗雷德霍姆性质可能取决于系统方程中涉及的出生率和死亡率之间的竞争结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Arnold Mathematical Journal Mathematics-Mathematics (all)

CiteScore

1.50

自引率

0.00%

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期刊介绍： The Arnold Mathematical Journal publishes interesting and understandable results in all areas of mathematics. The name of the journal is not only a dedication to the memory of Vladimir Arnold (1937 – 2010), one of the most influential mathematicians of the 20th century, but also a declaration that the journal should serve to maintain and promote the scientific style characteristic for Arnold''s best mathematical works. Features of AMJ publications include: Popularity. The journal articles should be accessible to a very wide community of mathematicians. Not only formal definitions necessary for the understanding must be provided but also informal motivations even if the latter are well-known to the experts in the field. Interdisciplinary and multidisciplinary mathematics. AMJ publishes research expositions that connect different mathematical subjects. Connections that are useful in both ways are of particular importance. Multidisciplinary research (even if the disciplines all belong to pure mathematics) is generally hard to evaluate, for this reason, this kind of research is often under-represented in specialized mathematical journals. AMJ will try to compensate for this.Problems, objectives, work in progress. Most scholarly publications present results of a research project in their “final'' form, in which all posed questions are answered. Some open questions and conjectures may be even mentioned, but the very process of mathematical discovery remains hidden. Following Arnold, publications in AMJ will try to unhide this process and made it public by encouraging the authors to include informal discussion of their motivation, possibly unsuccessful lines of attack, experimental data and close by research directions. AMJ publishes well-motivated research problems on a regular basis. Problems do not need to be original; an old problem with a new and exciting motivation is worth re-stating. Following Arnold''s principle, a general formulation is less desirable than the simplest partial case that is still unknown.Being interesting. The most important requirement is that the article be interesting. It does not have to be limited by original research contributions of the author; however, the author''s responsibility is to carefully acknowledge the authorship of all results. Neither does the article need to consist entirely of formal and rigorous arguments. It can contain parts, in which an informal author''s understanding of the overall picture is presented; however, these parts must be clearly indicated.

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