Retarded differential equations with piecewise constant delays
Retarded differential equations with piecewise constant delays
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DOI：
10.1016/0022-247x(84)90248-8
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发表时间：
1984-03
影响因子：
1.3
通讯作者：
K. Cooke;J. Wiener
中科院分区：
文献类型：
--
作者：
K. Cooke;J. Wiener
泛函与泛函微分方程之间存在着深刻而密切的联系。因此，研究第一个往往使人们能够预测中立型微分方程的性质。另一方面，对于后者的一些方法，在特殊情况下，当参数的偏差在个别点为零时，已被用于研究函数方程[11]。函数方程与离散（例如整数值）变量的差分方程直接相关，其理论在书[2]和许多后续论文中得到了非常深入的发展。与差分方程相邻的是带冲击的脉冲泛函微分方程和开关、负载方程（即，对于给定的自变量常数值，包括未知解的值的那些方程），具有滞后自变量形式h（t）=[f]的方程，即，具有恒定区间，这类方程的实质性理论实际上尚未发展[31]。本文研究了变元为h（t）=[t]，h（t）=[rn]和h（t）= t-n [t]的微分方程。第二节考虑了具有两个时滞[t]和[t-11]的常系数线性方程组。初始值问题在t=-1和t= 0时提出，并在t> 0时寻求解。解的存在唯一性及其265
Profound and close links exist between functional and functional differential equations. Thus, the study of the first often enables one to predict properties of differential equations of neutral type. On the other hand, some methods for the latter in the special case when the deviation of the argument vanishes at individual points have been used to investigate functional equations [11. Functional equations are directly connected with difference equations of a discrete (for example, integer-valued) argument, the theory of which has been very intensively developed in the book [2] and in numerous subsequent papers. Bordering on difference equations are the impulse functional differential equations with impacts and switching, loaded equations (that is, those including values of the unknown solution for given constant values of the argument), equations with lagging arguments of the form h (t)=[f], that is, having intervals of constancy, etc. A substantial theory of such equations is virtually undeveloped [3 1.In this paper we study differential equations with arguments h (t)=[t], h (t)=[rn], and h (t)= t-n [t]. In the second section, linear equations with constant coefficients and two delays,[t] and [t-11, are considered. The initial-value problem is posed at t=-1 and t= 0, and the solution is sought for t> 0. The existence and uniqueness of solution and of its 265