摘要：
Under the Banach contraction mapping principle, the following one order nonlinear neutral delay differential equations (NDE):d/dt[x (t) +cx (t-τ) ]+f (t, x (t-σ) , x (t-δ)) =g (t) , t≥t0, Where c∈R, τ, σ, δ>0, f∈C ([t0, ∞) ×R2, R) , and g∈C ([t0, ∞) , R+).proves several existence results of nonoscillatory solutions for the above equation (NDE) , building a few Mann iterative approximation for these nonoscillatory solutions.This paper also explores several error estimates between the approximate solutions and the nonoscillatory solutions.%利用Bannach压缩映射原理,考虑如下一阶非线性中立时滞微分方程(NDE):d/dt[x(t)+cx(t-τ)]+f(t,x(t-σ),x(t-δ))=g(t),t≥t0,其中,c∈R,τ,σ,δ>0,f∈C([t0,∞)×R2,R),g∈C([t0,∞),R+),证明了上述非线性中立时滞微分方程(NDE)非振荡解的存在性定理,建立了Mann型迭代逼近.同时,讨论了逼近解和非振荡解之间的误差估计.
