Oscillation results for third order nonlinear mixed neutral differential equations

Abstract

In this paper, the authors study oscillatory and asymptotic behavior of solutions of class of nonlinear third order neutral differential equations with positive and negative coefficients o the for 0≤a(t)(b(t)(y(t) +p(t)y(t)) + q(t)G(y(t)) ? h(t)H(y(t)= 0 (E for 0 ≤ p(t) < p1 < 1 and ?1 < p2 ≤ p(t) ≤ 0. The results in this paper generalize the result of [LI, T.-ZHANG, C.-XING, G.: Oscillation of third-order neutral delay differential equations Abstr. Appl. Anal. 2012 (2012), Article ID 569201] and various results in the literature. We establis new conditions which guarantees that every solutions of (E) either oscillatory or converges to zero Examples are considered to illustrate the main results.