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Applicable Analysis
An International Journal
Volume 91, 2012 - Issue 7
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Original Articles

Strict stability in terms of two measures for impulsive differential equations with ‘supremum’

Ravi P. Agarwal Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, FL 32901, USA; Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi ArabiaCorrespondence[email protected]
&
Snezhana Hristova Department of Applied Mathematics and Modeling, Plovdiv University, Plovdiv 4000, Bulgaria
Pages 1379-1392 | Received 01 Mar 2011, Accepted 02 Mar 2011, Published online: 07 Jul 2011
 
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Abstract

Strict stability for a nonlinear system of impulsive differential equations with ‘supremum’ is defined and studied. Razhumikhin method with piecewise continuous scalar Lyapunov functions and comparison results for scalar impulsive differential equations are the bases of the main proofs. To unify a variety of stability concepts and to offer a general framework for the investigation of the stability theory, the notion of stability in terms of two measures has been applied. An example illustrating the usefulness of the obtained sufficient conditions is also included.

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Acknowledgements

The research was partially supported by the Grant MU11FMI005/29.05.2011.

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