Almost Periodic Differential Equations
Almost Periodic Differential Equations
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DOI：
10.1007/bfb0070324
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发表时间：
1974-06
期刊：
影响因子：
--
通讯作者：
A. Fink
中科院分区：
文献类型：
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作者：
A. Fink
这些讲义是写的希望，最近的进展，在这个问题上的几乎周期微分方程可以成为更容易获得的，如果基本事实收集在一个地方。众所周知，在天体力学中，概周期解和稳定解是密切相关的。同样地，稳定的电子电路表现出几乎周期性的行为。大量的研究都是为了研究这些现象。在我们的参考书目中大约五百条中，有很大一部分是1955年以后的。这些讲义是关于常微分方程的概周期解的。我花了前四章的理论几乎周期函数。在这些章节中包括了概周期理论的框架。我采取的策略是只介绍与后面几章讨论微分方程有密切关系的材料。我基本上不包括几乎周期函数的事实，这不是用来证明别的东西。这不是美德。它说明了这里所发展的理论的深度。除了关于微分方程解的存在性和唯一性的通常初步事实之外，这些笔记是独立的。因此，它应该向广大受众开放。我已经采取了周期性的情况下，作为动机的大部分材料，所以熟悉傅立叶级数理论的周期函数是有帮助的。
These lecture notes are written with the hope that the recent advances in the subject of almost periodic differential equations can become more accessible if the basic facts are collected in one place. It is well known that in Celestial Mechanics, almost periodic solutions and stable solutions are intimately related. In the same way, stable electronic circuits exhibit almost periodic behavior. A vast amount of research has been directed toward studying these phenomena. A great portion of the roughly five hundred items in our bibliography are dated after 1955.These lecture notes are about almost periodic solution to ordinary differential equations. I spend the first four chapters on the theory of almost periodic functions. Included in those chapters is the skeleton of almost periodic theory. I have taken the tack of presenting only that material which is germane to the later chapters on differential equations. I include essentially no fact about almost periodic functions which is not used to prove something else. This is no virtue. It illustrates the depth of the thoery that is developed here. These notes are self-contained except for the usual preliminary facts about existence and uniqueness of solutions of differential equations. It should therefore be accessible to a wide audience. I have taken the periodic case as motivation for much of the material, so an acquaintance with the fourier series theory of periodic functions is helpful.