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International Journal of Mathematics and Mathematical Sciences
Volume 21 (1998), Issue 3, Pages 493-497
http://dx.doi.org/10.1155/S0161171298000702

Necessary and sufficient conditions for the oscillation of delay differential equation with a piecewise constant argument

Department of Mathematics, Faculty of Education, Ain Shams University, Roxy , Cairo, Egypt

Received 13 August 1996; Revised 18 March 1997

Copyright © 1998 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The characteristic equation for an equation with continuous and piecewise constant argument in the form x˙(t)+px(tτ)+qx([tk])=0where p,q,τ+and k is presented, which when q=0 reduces to f(λ)=λ+eλτ=0 and when p=0 reduces to λ1+qλk=0. Also, the necessary and sufficient conditions for oscillation are obtained.