New results on the qualitative analysis of solutions of VIDEs by the Lyapunov–Razumikhin technique

Osman Tunç; E.  Korkmaz

doi:10.37863/umzh.v74i11.6083

Osman Tunç Van Yuzuncu Yil Univ., Turkey https://orcid.org/0000-0003-2965-4561
E. Korkmaz Muş Alparslan Univ., Turkey

DOI: https://doi.org/10.37863/umzh.v74i11.6083

Анотація

УДК 517.9

Нові результати з якісного аналізу розв'язків ІДРВ за методикою Ляпунова–Разуміхіна

Розглянуто нову математичну модель, що описується інтегро-диференціальним рівнянням Вольтерра (ІДРВ) зі сталим запізненням. За допомогою техніки Ляпунова–Разуміхіна отримано нові прийнятні умови рівномірно асимптотичної стійкості, обмеженості та квадратичної інтегровності розв'язків цього ІДРВ. Встановлені умови покращують деякі попередні результати, а також є їх нелінійними узагальненнями. Крім того, вони слабші, ніж деякі результати, доступні в бібліографії цієї статті. Наведено два приклади, щоб продемонструвати можливе застосування цих результатів і введених концепцій. Використання техніки Ляпунова–Разуміхіна приводить до значних відмінностей та надає певну перевагу порівняно з відповідними методами, що використовуються в книгах і статтях, наведених у бібліографії.

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