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Bulletin of the London Mathematical Society 2003 35(2):239-246; doi:10.1112/S0024609302001662
© 2003 by London Mathematical Society
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© London Mathematical Society

Oscillation Criteria for First-Order Delay Equations

Y. G. Sficas and I. P. Stavroulakis

Department of Mathematics, University of Ioannina 451 10 Ioannina, Greece
Department of Mathematics, University of Ioannina 451 10 Ioannina, Greece; ipstav{at}cc.uoi.gr

Received 18 September 2001. Revision received 4 April 2002.

This paper is concerned with the oscillatory behaviour of first-order delay differential equations of the form


Formula
(1)

whereFormula is non-decreasing, {tau}(t) < t for t ≥t0 and Formula. Let the numbers k andL be defined by


Formula

It is proved here that when L < 1 and 0 < k ≤ 1/e all solutions of equation (1) oscillate in several cases in which the condition


Formula

holds, where {lambda}1 is the smaller root of the equation {lambda} = ek{lambda}. 2000 Mathematics Subject Classification 34K11 (primary); 34C10 (secondary).


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