OSCILLATIONS OF 1ST-ORDER NEUTRAL DIFFERENTIAL-EQUATIONS WITH VARIABLE-COEFFICIENTS

Consider the first-order neutral delay differential equation d/dt [x(t ) - P(t) x(t - tau)] + Q(t) x(t - delta(t)) = 0, t greater-than-or-equ al-to t0, where tau > 0, P, Q, delta is-an-element-of C([t0, infinity) , R+), and lim(t --> infinity) (t - delta(t)) = infinity. First we obt ain a necessary and sufficient condition for the oscillation of all so lutions of this equation. And then some applications of this result ar e listed. Our results can improve many known results in the literature . (C) 1994 Academic Press, Inc.