Oscillation criteria for a class of second-order neutral delay differential equations

In this article, we investigate oscillation and asymptotic behaviour of all solutions of a class of neutral delay differential equations of second-order with several positive and negative coefficients having the formx(t)±∑i∈Rri(t)x(αi(t))″+∑i∈Ppi(t)x(βi(t))-∑i∈Qqi(t)x(γi(t))=f(t)fort⩾t0,where R,P,QR,P,Q are bounded beginning segments of positive integers, ri∈C([t0,∞),R+)ri∈C([t0,∞),R+), pi,qi∈C([t0,∞),R+)pi,qi∈C([t0,∞),R+), αi,βi,γi∈C([t0,∞),R)αi,βi,γi∈C([t0,∞),R) are delay functions and f is a continuous function. Our results improve and extend the recent results given in the papers [J. Manojlović, Y. Shoukaku, T. Tanigawa, N. Yoshida, Oscillation criteria for second-order differential equations with positive and negative coefficients, Appl. Math. Comput. 181 (2006) 853–863] and [A. Weng, J. Sun, Oscillation of second order delay differential equations, Appl. Math. Comput. 198 (2) (2008) 930–935].