Existence of nonoscillatory solutions of higher-order neutral differential equations with positive and negative coefficients

In this paper, we consider the following higher-order neutral functional differential equations with positive and negative coefficients: d(n)/dt(n) [x(t) + cx (t-tau)] + (-1)(n+1) [P(t)x(t-sigma) - Q (t)x(t-delta)] = 0, t greater than or equal to t(0), where n greater than or equal to 1 is an integer, c is an element of R, tau, sigma, delta is an element of R+, and P, Q is an element of C([t(0), infinity), R+), R+ = [0, infinity). We obtain the global results (with respect to c) which are some sufficient conditions for the existence of nonoscillatory solutions. (C) 2002 Elsevier Science Ltd. All rights reserved.