# Existence for nonoscillatory solutions of higher order nonlinear neutral differential equations

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## Abstract

Consider the forced higher-order nonlinear neutral functional differential equation where

$$\frac{{d^n }}{{dt^n }}\left[ {x\left( t \right) + C\left( t \right)x\left( {t - \tau } \right)} \right] + \sum\limits_{i = 1}^m {Q_i } \left( t \right)f_i \left( {x\left( {t - \sigma _i } \right)} \right) = g\left( t \right),\quad t \geqslant t_0 ,$$

*n*,*m*≥, 1 are integers, τ, σ_{i}∈ 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.## Keywords

neutral differential equations nonoscillatory solutions## Preview

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