一类高维时滞微分方程的周期解

本文考虑高维时滞微分方程ｘ′（ｔ）＝Ａ（ｔ,ｘ（ｔ））ｘ（ｔ）＋ｆ（ｔ,ｘ（ｔ－ｒ（ｔ）））其中（ｔ,ｘ）∈Ｒ^ｎ,Ａ（ｔ,ｘ）是ｎ×ｎ连续矩阵,ｆ（ｔ,ｘ）是ｎ维连续向量,ｒ（ｔ）是时间依赖的滞量,应用不动点定理,在确定的条件下,证明了该系统的周期解的存在性与唯一性     

二阶无穷时滞泛函微分方程的正周期解

应用Krasnoselskii不动点定理讨论二阶无穷时滞泛函微分方程(t)+a(t)x(t)=f(t,xt)的正ω-周期解的存在性.     

一类高阶中立型泛函微分方程周期解的存在性

研究了一类高阶非线性中立型泛函微分方程x~((2n))(t)+cx~((2n))(t-τ)+f(x)x′+bx(t)+g(x(t-σ))=p(t)周期解的存在性,利用分析技巧结合重合度理论给出了该方程存在周期解的充分性定理.     

无限时滞线性中立型泛函微分方程周期解 (英)

本文以Cg空间为相空间,证明了具无限时滞D算子型线性中立型泛函微分方程存在周期解当且仅当存在有界解,得到了与以往结论互不包含的结果．     

无穷时滞的泛函微分方程的多重正周期解(英文)

In this paper, we investigate the existence of multiple positive periodic solutions for functional differential equations with infinite delay by applying the Krasnoselskii fixed point theorem for cone map and the Leggett-Williams fixed point theorem.     

Legendre-Gauss Spectral Collocation Method for Second Order Nonlinear Delay Differential Equations

In this paper, we present and analyze a single interval Legendre-Gauss spectral collocation method for solving the second order nonlinear delay differential equations with variable delays. We also propose a novel algorithm for the single interval scheme and apply it to the multiple interval scheme for more efficient implementation. Numerical examples are provided to illustrate the high accuracy of the proposed methods.     

一类非齐次时滞微分方程概周期解的存在性

该文研究一类非齐次时滞微分方程的概周期解，结合运用指数二分法，给出了系统存在概周期解的一组充分条件．     

非自治时滞微分方程的正周期解

By utilizing a fixed point theorem on cone,some new results on the existence of positive periodic solutions for nonautonomous differential equations with delay are derived.     

三阶泛函微分方程的周期解

利用Brouwer度理论得到了泛函微分方程x′″（t） ∑i=0^2[αix(i)(t) bix(i)(t-τi)] g1(x(t)) g2(x(t-τ））=p（t）存在2π周期解的充分性条件，推广了[1]中的有关结果．     

具无限时滞线性中立型泛函微分方程周期解

本文证明了具无限时滞D算子型线性中立型泛函微分方程存在周期解当且仅当存在有界解,推广了MasseraJ．L,ChowS．N．和MakayM．的结果．     

On the Attainable Order of Collocation Methods for Delay Differential Equations with Proportional Delay

To analyze the attainable order of m-stage implicit (collocation-based) Runge-Kutta methods for the delay differential equation (DDE) y′(t) = by(qt), 0 < q ≤ 1 with y(0) = 1, and the delay Volterra integral equation (DVIE) y(t) = 1 + $\tfrac{b}{q}\int {_0^{qt} }$ y(s) ds with proportional delay qt, 0 < q ≤ 1, our particular interest lies in the approximations (and their orders) at the first mesh point t = h for the collocation solution v(t) of the DDE and the iterated collocation solution u _it(t) of the DVIE to the solution y(t). Recently, H. Brunner proposed the following open problem: “For m ≤ 3, do there exist collocation points c _i = c _i(q), i = 1, 2,..., m in [0,1] such that the rational approximant v(h)is the (m, m)-Padé approximant to y(h)? If these exist, then |v(h) ? y(h)| = O(h ^2m+1) but what is the collocation polynomial M _m(t; q) = K Π _i=1 ^m (t ? c _i) of v(th), t ∈ [0, 1]?” In this paper, we solve this question affirmatively, and give the related results between the collocation solution v(t) of the DDE and the iterated collocation solution u _it(t) of the DVIE. We also answer to Brunner's second open question in the case that one collocation point is fixed at the right end point of the interval.     

关于退化中立型微分方程的周期解

讨论了退化中立型微分方程的周期解问题,给出了周期解存在性的条件和二维退化中立型微分方程周期解存在的代数判据,并且举例说明了其应用.     

A Branching Method for Studying Stability of a Solution to a Delay Differential Equation

We study stability of antisymmetric periodic solutions to delay differential equations. We introduce a one-parameter family of periodic solutions to a special system of ordinary differential equations with a variable period. Conditions for stability of an antisymmetric periodic solution to a delay differential equation are stated in terms of this period function.     

一类二阶微分方程周期解的存在性

研究二阶非线性滞后型微分方程x。(t)+P[x(。t)]+Q[x(。t)]R[x(t-r)]=f(t)通过Lyaponov方法给出了ω-周期解的存在性定理和时滞范围的简明表达式,推广了一些原有结果.     

Positive Periodic Solution for a Nonautonomous Delay Differential Equation

In this paper, by using the Krasnoselskii fixed point theorem, we study the existence of one or multiple positive periodic solutions of a nonautonomous delay differential equation. We also give some examples to demonstrate our results.     

多时滞高阶微分方程的周期解

By Fourier analysis techniques and Schauder fixed point theorem, we study the existence of periodic solutions for a class of even order differential equations with multiple delays. The result obtained is a generalization of the results developed by W. Layton to the case of multiple delays.     

一类具无穷时滞泛函微分方程的周期解

讨论具有无穷时滞中立型泛函微分方程$ \frac{\rm d}{{\rm d}t}\left(x(t)-\int_{-\infty}^{0}g(s,x(t+s)){\rm d}s\right) =A(t,x(t))x(t)+f(t,x_t)$的周期解问题,利用重合度理论中的延拓定理得到了周期解的存在性和唯一性条件;特别地,当$g(s,x)\equiv 0, A(t,x)=A(t)$时, 给出了存在唯一稳定周期解的条件.     

二阶非线性中立型泛函微分方程周期解的存在性

利用κ-集压缩算子拓扑度抽象连续定理,研究了一类二阶泛函微分方程周期解的存在性,获得了方程周期解存在的充分条件,这些结果推广并改进了已有文献的相关结果.     

泛函微分方程周期解的非回复性定理

nonrecurrence theorem on the existence of periodic solutions for functional differential equations is proved by employing the topological method, and some applications are given.     

泛函微分方程多个正周期解的存在性

考虑一类一阶非线性泛函微分方程,利用锥中的不动点理论给出存在多个正周期解的一些新的充分条件.