About maximum principles for one of the components of solution vector and stability for systems of linear delay differential equations

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2011, 2011(Special): 373-380. doi: 10.3934/proc.2011.2011.373

About maximum principles for one of the components of solution vector and stability for systems of linear delay differential equations

A. Domoshnitsky ^1,

1.	Department of Mathematics, Ariel University Center, Ariel, Israel

Received August 2010 Revised February 2011 Published October 2011

Abstract
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Under a Creative Commons license

In this paper we dene and discuss maximum principles for systems of delay dierential equations. Assertions on dierential inequalities for one of the components of solution vector are proven. On this basis new exponential stability results are obtained. In contrast with other results of this sort we do not assume the dominance of the main diagonal in order to get the exponential stability. Various tests of the exponential stability are proposed.

Keywords: Maximum principles, Cauchy matrices, exponential stability, positivity of Cauchy matrices.

Mathematics Subject Classification: 34K20, 34K38.

Citation: A. Domoshnitsky. About maximum principles for one of the components of solution vector and stability for systems of linear delay differential equations. Conference Publications, 2011, 2011 (Special) : 373-380. doi: 10.3934/proc.2011.2011.373

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