含时滞导数项的高阶中立型微分方程的正周期解  

Positive Periodic Solutions for Higher-order Neutral Functional Differential Equations with Delayed Derivative Terms

作　　者：赵明睿 

机构地区：[1]西北师范大学数学与统计学院,甘肃兰州730070

出　　处：《河北师范大学学报（自然科学版）》2016年第2期98-105,共8页Journal of Hebei Normal University：Natural Science

基　　金：国家自然科学基金(11261053);甘肃省自然科学基金(1208R-JZA129)

摘　　要：研究了高阶中立型时滞微分方程dn'dtn(u(t)-cu(t-δ))+M(u(t)-cu(t-δ))=f(t,u(t),u′(t-τ(t)),…,u(n-1)(t-τ(t)))正ω-周期解的存在性.通过构造一个特殊的锥,运用锥上的不动点指数理论,获得了该问题正周期解存在性的结果.In this paper,the existence of positive periodic solutions for higher-order neutral functional differential equations with delay dn/dt^n（u（t）-cu（t-δ））＋M（u（t）-cu（t-δ））=f（t,u（t）,u′（t-τ（t））,…,u^（n-1）（t-τ（t）））was considered.Since a special cone was constructed,the existence results of positive solutions of the equation was obtained by using the fixed point index theory in cones.

关 键 词：中立型泛函微分方程 正周期解 凸锥 不动点指数 

分 类 号：O175.15[理学—数学]