Publication Cover
Applicable Analysis
An International Journal
Volume 35, 1990 - Issue 1-4
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Original Articles

Invariant cones of positive initial functions for delay differential equations

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Pages 21-41 | Published online: 02 May 2007
 

Abstract

Consider the scalar delay differential equation x(t) + ∑ akx(t-rk) = 0 (1) where ak and rk ≥ 0, (0 ≤k ≤ m), are real numbers.In this paper we show that there exists an invariant cone of the positive initial functions if and only if the characteristic equation of Eq. (1) has a real root. We also give the constraction of the maximal invariant cone among the positive initial functions with respect to Eq. (1). At the end of the paper we show the generalizations of these results for systems

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