RLgEVIER Available online at www.sciencedirect.com MATHEMATICAL AND OClIENOI C~.' RRO'lr° COMPUTER MODELLING Mathematical and Computer Modelling 41 (2005) 417-461 www.elsevier.com/locate/mcm Oscillation of Functional Differential Equations R. P. AGARWAL Department of Mathematical Sciences Florida Institute of Technology Melbourne, FL 32901, U.S.A. agarwal@f it. edu S. R. GRACE Department of Engineering Mathematics Faculty of Engineering, Cairo University Orman, Giza 12221, Egypt srgrace©eng, cu. edu. eg I. KIGURADZE A. Razmadze Mathematical Institute of the Georgian Academy of Sciences Tbilisi, Georgia kig©rmi, acnet, ge D. O'REGAN Department of Mathematics National University of Ireland Galway, Ireland donal, oregan@nuigalway, ie (Received May 2004; accepted June 2004) Abstract--Some new criteria for the oscillation of functional differential equations of the form, d[ 1 d i d a d ]~ an--l(t) -~ an-2(t) d-t"'al(t) dt x(t) +Sq(t) f(x[g(t)])=O, are presented in this paper. © 2005 Elsevier Ltd. All rights reserved. Keywords--Oscillation, Nonoscillation, Functional, Nonlinear, Comparison. 1. INTRODUCTION In this paper, we are concerned with the oscillatory behavior of all solutions of the functional differential equation, Lnx (t) + 5q (t) f (x [g (t)]) = 0, (1.1; 5) 0895-7177/05/$ - see front matter (~) 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.mcm. 2004.06.018 Typeset by A~ts-~X