Stability tests and solution estimates for non-linear differential equations

An International Journal of Optimization and Control: Theories & Applications

article

Osman Tunç¹ 

[1] Van Yuzuncu Yil University

关键词: Delay differential equations;    Ordinary differential equations;    Lyapunov-Krasovskiĭ functional method;    Second method of Lyapunov;   

DOI  :  10.11121/ijocta.2023.1251

学科分类：地球科学(综合)

来源: Balikesir University

【 摘 要 】

This article deals with certain systems of delay differential equations (DDEs) and a system of ordinary differential equations (ODEs). Here, five new theorems are proved on the fundamental properties of solutions of these systems. The results on the properties of solutions consist of sufficient conditions and they dealt with uniformly asymptotically stability (UAS), instability and integrability of solutions of unperturbed systems of DDEs, boundedness of solutions of a perturbed system of DDEs at infinity and exponentially stability (ES) of solutions of a system of nonlinear ODEs. Here, the techniques of proofs depend upon the Lyapunov- Krasovski? functional (LKF) method and Lyapunov function (LF) method. For illustrations, in particular cases, four examples are constructed as applications. Some results of this paper are given at first time in the literature, and the other results generalize and improve some related ones in the literature.

【 授权许可】

CC BY