Forced oscillation of nth-order functional differential equations

In this paper we investigate the oscillation of forced functional different ial equations x((n))(t) + a(t)f(x(q(t))) = e(t), when the forcing term e(t) is not required to be the nth derivative of an oscillatory function. Some new oscillatory criteria are given. We also apply our technique to the forc ed neutral differential equation of the form (x(t) + cx(t - tau))((n)) + a(t)x(t) + b(t)x(t - tau) = e(t) + c(t)f(l)(x(t)) + d(t)f(2)(x(t - tau)), where xf(1)(x) > 0 and xf(2)(x) > 0 for x not equal 0; n greater than or eq ual to 1; tau, delta arc nonnegative constants; a(t) > 0; b(t) > 0; c(t) > 0; d(t) > 0; which includes the special case fj(x) /x/(lambda) sgn x, f(2)( x) = /x/(theta) sgn x, lambda not equal 1 and theta not equal 1. (C) 2001 A cademic Press.