摘要：
Applying the Krasnoselskii’s fixed point theorem of the sum of a completely continuous operator and a contractive operator,we discussed the existence of positive 2π-periodic solutions for the higher-order neutral differential equation d dt n (u(t)-cu (t -δ))+M(u(t)-cu (t -δ))=f (t,u(t -τ1 ),…,u(t -τm )), n whereδ>0,0 0 are constants,f :ℝ×[0,∞)m →[0,∞)is a continuous function which is 2π-periodic for t and τ1 ,τ2 ,…,τm ≥ 0 are constants.Existence and multiplicity results of positive periodic solutions were obtained for the equation.%用全连续算子与压缩算子和的 Krasnoselskii 不动点定理研究高阶中立型时滞微分方程d n dt n (u(t)-cu (t -δ))+M(u(t)-cu (t -δ))=f (t,u(t -τ1),…,u(t -τm ))正2π-周期解的存在性,其中：δ>0；00为常数；f ：ℝ×[0,∞) m →[0,∞)连续,关于 t 以2π为周期；τ1,τ2,…,τm ≥0为常数,获得了该方程正周期解的存在性与多重性结果。
