IJPAM: Volume 108, No. 1 (2016)

A CRITERION TO UNIFORM STABILITY FOR
FUNCTIONAL PERTURBED DIFFERENTIAL EQUATIONS

A. Ahmad$^1$, K. Haider, N. Javad, A. Zeinev$^4$
$^1$Abdus Salam School of Mathematical Sciences (ASSMS)
68-B, New Muslim Town
Lahore, PAKISTAN
$^4$Department of Mathematics
University of Chemical Technology and Metallurgy
8 ``St. Kl. Ohridski'', Blvd., Sofia 1756, BULGARIA


Abstract. In this paper we consider a class of non autonomous ODEs with a functional perturbation. For the unperturbed equation a Lyapunov function bounded by two quadratic forms is known. The Lipschitzean rate of the vector field along with some additional requirements to the derivatives of the Lyapunov function guarantee existence of uniform stable solutions. A sufficient condition that guarantees uniform stability of the zero-solution to the equation under consideration is discussed.

Received: March 12, 2016

AMS Subject Classification: 35R12, 35K50

Key Words and Phrases: functional differential equations, stability, Lyapunov function, functional perturbation

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DOI: 10.12732/ijpam.v108i1.11 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2016
Volume: 108
Issue: 1
Pages: 107 - 122


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