New and Improved Criteria on Fundamental Properties of Solutions of Integro—Delay Differential Equations with Constant Delay

Mathematics

Osman Tunç¹  Cemil Tunç²  Yuanheng Wang³  Jen-Chih Yao⁴ 

[1] Department of Computer Programing, Baskale Vocational School, Van Yuzuncu Yil University, Van 65080, Turkey;Department of Mathematics, Faculty of Sciences, Van Yuzuncu Yil University, Van 65080, Turkey;Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China;Research Center for Interneural Computing, China Medical University Hospital, China Medical University, Taichung 404332, Taiwan;

关键词: non-linear system;    IDDEs;    constant delay;    LKF;    stability;    instability;   

DOI  :  10.3390/math9243317

来源: DOAJ

【 摘 要 】

This paper is concerned with certain non-linear unperturbed and perturbed systems of integro-delay differential equations (IDDEs). We investigate fundamental properties of solutions such as uniformly stability (US), uniformly asymptotically stability (UAS), integrability and instability of the un-perturbed system of the IDDEs as well as the boundedness of the perturbed system of IDDEs. In this paper, five new and improved fundamental qualitative results, which have less conservative conditions, are obtained on the mentioned fundamental properties of solutions. The technique used in the proofs depends on Lyapunov-Krasovski functionals (LKFs). In particular cases, three examples and their numerical simulations are provided as numerical applications of this paper. This paper provides new, extensive and improved contributions to the theory of IDDEs.

【 授权许可】

Unknown