Existence of nonoscillatory solutions of higher-order neutral differential equations with positive and negative coefficients

Throughout this paper, the following conditions are assumed to hold. () n≥  is a positive integer, r ∈ C([t,∞),R+),  < a < b, τ > , σ > ; () p ∈ C([t,∞)× [a,b],R), q ∈ C([t,∞),R+), q ∈ C([t,∞),R+), h ∈ C([t,∞),R); () (u) is a continuously increasing real function with respect to u defined on R, and –(u) satisfies the local Lipschitz condition; () gi ∈ C(R,R), gi(u) satisfy the local Lipschitz condition and ugi(u) > , i = , , for u = . Recently there have been a lot of activities concerning the existence of nonoscillatory solutions for neutral differential equationswith positive and negative coefficients. In , Zhou and Zhang [] studied the higher-order linear neutral delay differential equation