The oscillation of higher-order differential equations with deviating arguments

In this paper, some new criteria for the oscillation of higher-order functi onal differential equations of the form L(n)x(t) + F(t, x(g(t))) = 0, n is even are established. Some of our results are obtained via comparing it with sec ond-order ordinary linear and first-order delay differential equations. The oscillation of this equation when n is odd is also considered. Then, we sh all use the obtained results to study the oscillatory behavior of the neutr al functional differential equations of the form L(n)x(t) + c(t)x(tau(t))) + F(t,x(g(t))) = 0, n is even and the damped functional differential equations of the type L(n)x(t) + H(t,x(g(t)), d/dt x(h(t))) = 0, n is even. The obtained results extend, improve, and correlate a number of existing cr iteria. (C) 1999 Elsevier Science Ltd. All rights reserved.