We consider the integro differential equation
where , are piecewise continuous functions and is a positive constant. We establish sufficient conditions guaranteeing either asymptotic stability or uniform asymptotic stability for the zero solution. These conditions state that the instantaneous stabilizing term on the right-hand side dominates in some sense the perturbation term with delays. Our conditions not require being bounded from above. The results are based on the method of Lyapunov functionals and Razumikhin functions.
Submitted October 5, 2016. Published November 25, 2016.
Math Subject Classifications: 34K20, 34K27, 34D20.
Key Words: Annulus argument; uniform asymptotic stability.
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| László Hatvani |
University of Szeged, Bolyai Institute
Aradi vértanúk tere 1
H-6720 Szeged, Hungary
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