一阶非线性中立时滞微分方程非振荡解的研究

On the Nonoscillatory Solutions of One Order Nonlinear Neutral Delay Differential Equations

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.

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,∞)×R^2,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.