Asymptotic behavior of a class of perturbed differential equations | Zendy

A. Dorgham | Zendy; Mekki Hammi | Zendy; Mohamed Ali Hammami | Zendy

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Asymptotic behavior of a class of perturbed differential equations

Author(s) -

A. Dorgham,

Mekki Hammi,

Mohamed Ali Hammami

Publication year - 2021

Publication title -

ukrains’kyi matematychnyi zhurnal

Language(s) - English

Resource type - Journals

ISSN - 1027-3190

DOI - 10.37863/umzh.v73i5.232

Subject(s) - exponential stability , mathematics , nonlinear system , lyapunov function , class (philosophy) , mathematical analysis , ball (mathematics) , differential equation , asymptotology , method of matched asymptotic expansions , physics , computer science , quantum mechanics , artificial intelligence

UDC 517.9This paper deals with the problem of stability of nonlinear differential equations with perturbations. Sufficient conditions for global uniform asymptotic stability in terms of Lyapunov-like functions and integral inequality are obtained. The asymptotic behavior is studied in the sense that the trajectories converge to a small ball centered at the origin. Furthermore, an illustrative example in the plane is given to verify the effectiveness of the theoretical results.

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