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

Pages: 373 - 380, Issue Special, September 2011

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A. Domoshnitsky - Department of Mathematics, Ariel University Center, Ariel, Israel (email)

Abstract: In this paper we de ne and discuss maximum principles for systems of delay di erential equations. Assertions on di erential 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, positivity of Cauchy matrices, exponential stability
Mathematics Subject Classification:  34K20, 34K38

Received: August 2010;      Revised: February 2011;      Published: October 2011.