NECESSARY AND SUFFICIENT CONDITIONS FOR OSCILLATION OF AUTONOMOUS NEUTRAL DIFFERENTIAL-EQUATIONS WITH DISTRIBUTED DELAY

Authors
BAINOV D PETROV V
Citation
D. Bainov et V. Petrov, NECESSARY AND SUFFICIENT CONDITIONS FOR OSCILLATION OF AUTONOMOUS NEUTRAL DIFFERENTIAL-EQUATIONS WITH DISTRIBUTED DELAY, Journal of mathematical analysis and applications, 182(1), 1994, pp. 202-220
Citations number
11
Categorie Soggetti
Mathematics, Pure",Mathematics,Mathematics,Mathematics
Journal title
Journal of mathematical analysis and applications → ACNP
ISSN journal
0022247X
Volume
182
Issue
1
Year of publication
1994
Pages
202 - 220
Database
ISI
SICI code
0022-247X(1994)182:1<202:NASCFO>2.0.ZU;2-U
Abstract
In the paper the autonomous neutral differential equation with distrib uted delay d/dt[x(t)+delta1.integral/-tau/0 x(t-s) dr1(s)]+delta2.inte gral-tau/0 x(t-s) dr2(s)=0 is considered,where delta(i)= +/-1, i=1,2. It is proved that if r1(tau1-) not-equal r1(tau1+), then the necessary and sufficient condition for all solutions of this equation to oscill ate is that its corresponding characteristic equation z(1+delta1 integ ral-tau/0 e(-zs) dr1(s)) +delta2.integral-tau/0 e(-zs) dr2(s) 0 have n o real roots. (C) 1994 Academic Press, Inc.