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Stability Theory and the Existence of Periodic Solutions and Almost Periodic Solutions

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概要 Since there are several excellent books on stability theory, the author selected some recent topics in stability theory which are related to existence theorems for periodic solutions and for almost pe...riodic solutions. The author hopes that these notes will also serve as an introduction to stability theory. These notes contain stability theory by Liapunov's second method and somewhat extended discussion of stability properties in almost periodic systems, and the existence of a periodic solution in a periodic system is discussed in connection with the boundedness of solutions, and the existence of an almost periodic solution in an almost periodic system is considered in con nection with some stability property of a bounded solution. In the theory of almost periodic systems, one has to consider almost periodic functions depending on parameters, but most of text books on almost periodic functions do not contain this case. Therefore, as mathemati cal preliminaries, the first chapter is intended to provide a guide for some properties of almost periodic functions with parameters as well as for properties of asymptotically almost periodic functions. These notes originate from a seminar on stability theory given by the author at the Mathematics Department of Michigan State Univer sity during the academic year 1972-1973. The author is very grateful to Professor Pui-Kei Wong and members of the Department for their warm hospitality and many helpful conversations. The author wishes to thank Mrs.続きを見る
目次 I. Preliminaries
1. Liapunov Functions
2. Almost Periodic Functions
3. Asymptotically Almost Periodic Functions
4. Quasi-Periodic Functions
5. Boundary Value Problem
II. Stability and Boundedness
6. Stability of a Solution
7. Asymptotic Stability of a Solution
8. Boundedness of Solutions
9. Asymptotic Stability in the Large
10. Asymptotic Behavior of Solutions
11. Converse Theorems
12. Total Stability
13. Inherited Properties in Almost Periodic Systems
14. Uniformly Asymptotic Stability in Almost Periodic Systems
III. Existence Theorems for Periodic Solutions and Almost Periodic Solutions
15. Existence Theorems for Periodic Solutions
16. Existence Theorems for Almost Periodic Solutions
17. Separation Condition in Almost Periodic Systems
18. Uniform Stability and Existence of Almost Periodic Solutions
19. Existence of Almost Periodic Solutions by Liapunov Functions
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登録日 2020.06.27
更新日 2020.06.28