najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2024-15-6-749-754najo-118Research ArticleMATHEMATICSМАТЕМАТИКАSome conditions for the existence of 4-periodic solutions in non-homogeneous differential equations involving piecewise alternately advanced and retarded argumentsНекоторые условия существования 4-периодических решений в неоднородных дифференциальных уравнениях с кусочно-попеременно опережающими и запаздывающими аргументамиhttps://orcid.org/0000-0002-3823-5898ЧиуКуо-ШоуChiuKuo-Shou

Kuo-Shou Chiu – Departamento de Matem´atica, Facultad de Ciencias B´asicas

Jos´e Pedro Alessandri 774, Santiago

kschiu@umce.clhttps://orcid.org/0000-0001-6515-6880Кордова-ЛепеФ.Cordova-LepeF.

Fernando Cordova-Lepe – Departamento de Matem´atica, F´ısica y Estad´ıstica

Talca

Universidad Metropolitana de Ciencias de la Educaci´onChileUniversidad Cat´olica del MauleChile202405062025156749754Copyright © Chiu K., Cordova-Lepe F., 20252025Чиу К., Кордова-Лепе Ф.Chiu K., Cordova-Lepe F.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/118

The manuscript introduces a method to characterize 4-periodic solutions in first-order non-homogeneous differential equations involving piecewise alternately advanced and retarded argument. It systematically delineates the prerequisites for these solutions to exist and furnishes precise methodologies for their determination. Additionally, the paper includes the illustrative example, including scenarios with infinitely many solutions, to demonstrate the effectiveness of the proposed approach.

В рукописи представлен метод характеризации 4-периодических решений в неоднородных дифференциальных уравнениях первого порядка, включающих кусочно-попеременно опережающий и запаздывающий аргумент. Он систематически описывает предпосылки для существования этих решений и предоставляет точные методологии для их определения. Кроме того, в статью включен иллюстративный пример, включая сценарии с бесконечным количеством решений, для демонстрации эффективности предлагаемого подхода.

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The authors declare that there are no conflicts of interest present.