一类时标上具状态依赖时滞的中立型泛函微分方程的周期正解

数学物理学报 ›› 2010, Vol. 30 ›› Issue (3): 730-742.

一类时标上具状态依赖时滞的中立型泛函微分方程的周期正解

李永昆|张洪涛

云南大学数学系昆明 650091

收稿日期:2007-12-10 修回日期:2009-10-22 出版日期:2010-05-25 发布日期:2010-05-25
基金资助:
国家自然科学基金 (10971183)资助

Positive Periodic Solutions of Neutral Functional Differential Equations with State Dependent Delays on Time Scales

LI Yong-Kun, ZHANG Hong-Tao

Department of Mathematics, Yunnan University, |Kunming 650091

Received:2007-12-10 Revised:2009-10-22 Online:2010-05-25 Published:2010-05-25
Supported by:
国家自然科学基金 (10971183)资助

摘要/Abstract

摘要：

该文利用一个严格集压缩不动点定理, 得到了如下形式的一类时标上具状态依赖时滞的中立型泛函微分方程周期正解存在性的充分条件
x^Δ(t)=x(t)[r(t)-a(t)x(t)-∑ⁿ_j₌₁a_j(t) x(t-τ_j(t, x(t)))-∑ⁿ_j₌₁c_j(t) x^Δ(t-σ_j(t, x(t)))g ],
其中r, a, a_j, c_j∈C( T, R⁺)(j=1, 2, … , n) 是 ω - 周期函数, τ_j, σ_j∈C( T×R, T)(j=1, 2, … , n) 分别是其第一变元的$\omega$ -周期函数.

关键词: 周期正解, 中立型泛函微分方程, 时标, 严格集压缩

Abstract:

By using a fixed point theorem on strict-set-contraction, some sufficient conditions are obtained for the existence of positive periodic solutions for a periodic neutral functional differential equation on time scales of the form
x^Δ(t)=x(t)[r(t)-a(t)x(t)-∑ⁿ_j₌₁a_j(t) x(t-τ_j(t, x(t)))-∑ⁿ_j₌₁c_j(t) x^Δ(t-σ_j(t, x(t)))g ],
where r, a, a_j, c_j∈C( T, R⁺)(j =1, 2, … , n) are ω -periodic functions, and τ_j, σ_j∈C( T×R, T)(j =1, 2, … , n) are ω -periodic functions with respect to their first arguments, respectively.

Key words: Positive periodic solution, Neutral functional differential equation, Time scales, Strict-set-contraction

中图分类号:

34K13

李永昆, 张洪涛. 一类时标上具状态依赖时滞的中立型泛函微分方程的周期正解[J]. 数学物理学报, 2010, 30(3): 730-742.

LI Yong-Kun, ZHANG Hong-Tao. Positive Periodic Solutions of Neutral Functional Differential Equations with State Dependent Delays on Time Scales[J]. Acta mathematica scientia,Series A, 2010, 30(3): 730-742.

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