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Vietnam Journal of Mathematics 35:3(2007) 285-298 |
Instability of Impulsive Hybrid State Dependent Delay Differential Systems |
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Bashir Ahmad |
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Abstract. In this paper, we present the sufficient conditions ensuring the instability of the zero solution of an impulsive state dependent delay differential system for different conditions on the delay function. We assume the instability of the associated linear impulsive system and apply the idea of dichotomies together with Schauder--Tychonoff Theorem to establish the sufficient conditions for the unstable solution of the problem at hand. |
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2000 Mathematics Subject Classification: 4D20, 34K20, 34K45. |
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Keywords: Impulsive differential system, state dependent delay, $(h, k)$-dichotomies. |
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Vietnam Academy of Science and Technology
& Vietnamese Mathematical Society © Copyright 2009 Vietnam Journal of Mathematics. All rights reserved. |