Oscillation and Nonoscillation of Fourth-order Nonlinear Neutral Differential Equations with "Maxima".

Abstract

In this paper, we study the oscillation and asymptotic properties of fourth-order nonlinear neutral dierential equations with \maxima" (r(t)(y(t) + p(t)y(h(t)))00)00 + q(t) max [(t);t] f(y(s)) = 0; t t0 0 (0.1) and R 1 t0 1 r(t)dt = 1;we establish necessary and sucient conditions for all solutions of the equation (0.1) to be oscillatory.These results extend some known results in the literature without \maxima". Examples are given to illustrate the main results.