Existence for nonoscillatory solutions of higher order nonlinear neutral differential equations

Consider the forced higher-order nonlinear neutral functional differential equation $$\frac{{d^n }}{{dt^n }}\left[ {x\left( t \right) + C\left( t \right)x\left( {t - \tau } \right)} \right] + \sum\limits_{i = 1}^m {Q_i } \left( t \right)f_i \left( {x\left( {t - \sigma _i } \right)} \right) = g\left( t \right),\quad t \geqslant t_0 ,$$ where n,m ≥, 1 are integers, τ, σi ∈ ℝ+ = [0,∞), C,Q i, g ∈ C([t 0,∞), ℝ), fi ∈ C(ℝ, ℝ), (i = 1, 2, ...;, m). Some sufficient conditions for the existence of a nonoscillatory solution of above equation are obtained for general Q i(t) (i = 1, 2, ... ,m) and g(t) which means that we allow oscillatory Q i(t) (i = 1, 2, ... ,m) and g(t). Our results improve essentially some known results in the references.