一种高阶中立型方程正解的存在性

Exisitense of positive solutions for a kind higher order neutral differential equation

本文为了研究具有正、负系数的高阶中立型微分方程(x(t)-C(t)x(t-γ))(n)+P(t)x(t-τ)-Q(t)x(t-δ)=0正解的存在性,通过构造压缩算子,利用压缩映像原理证明了正解的存在性,找出了正解存在的充分条件。

This article discusses the existence of positive solution of the higher order neutral differential equations with positive and negative coefficients,and (x(t)-C(t)x(t-γ))(n)+P(t)x(t-τ)-Q(t)x(t-δ)=0 the compression operator are structured . The deflation principle is applied to prove the existence of the positive solution, and the sufficient conditions are found.