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

[摘要] In the paper the autonomous neutral differential equation with distributed delay d/dt[x(t)+delta1.integral/-tau/0 x(t-s) dr1(s)]+delta2.integral-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 oscillate is that its corresponding characteristic equation z(1+delta1 integral-tau/0 e(-zs) dr1(s)) +delta2.integral-tau/0 e(-zs) dr2(s) 0 have no real roots. (C) 1994 Academic Press, Inc.

[发布日期] 1994-02-15