河北师范大学学报—

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刊名：河北师范大学学报（自然科学版）Journal of Hebei Normal University (Natural Science)
主办：河北师范大学
ISSN： 1000-5854
CN： 13-1061/N
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含时滞导数项的高阶中立型微分方程的正周期解

赵明睿

西北师范大学数学与统计学院, 甘肃兰州 730070
DOI： 10.13763/j.cnki.jhebnu.nse.2016.02.002

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

ZHAO Mingrui

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摘要/Abstract

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.

Abstract：

In this paper,the existence of positive periodic solutions for higher-order neutral functional differential equations with delay
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)))
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

关键词： 中立型泛函微分方程 ; 正周期解 ; 凸锥 ; 不动点指数

Key words： neutral functional differential equations ; positive periodic solution ; cone ; fixed point index

参考文献 14

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