## ＜電子ブック＞Stability Theory and the Existence of Periodic Solutions and Almost Periodic Solutions

責任表示 by T. Yoshizawa Yoshizawa, T SpringerLink (Online service) English (英語) Springer New York 1975- New York, NY, United States シリーズ Applied Mathematical Sciences ; 14 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 I. Preliminaries1. Liapunov Functions2. Almost Periodic Functions3. Asymptotically Almost Periodic Functions4. Quasi-Periodic Functions5. Boundary Value ProblemII. Stability and Boundedness6. Stability of a Solution7. Asymptotic Stability of a Solution8. Boundedness of Solutions9. Asymptotic Stability in the Large10. Asymptotic Behavior of Solutions11. Converse Theorems12. Total Stability13. Inherited Properties in Almost Periodic Systems14. Uniformly Asymptotic Stability in Almost Periodic SystemsIII. Existence Theorems for Periodic Solutions and Almost Periodic Solutions15. Existence Theorems for Periodic Solutions16. Existence Theorems for Almost Periodic Solutions17. Separation Condition in Almost Periodic Systems18. Uniform Stability and Existence of Almost Periodic Solutions19. Existence of Almost Periodic Solutions by Liapunov FunctionsReferences.続きを見る http://hdl.handle.net/2324/1000907792 Full text available from SpringerLink ebooks - Mathematics and Statistics (Archive)

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レコードID 3641506 QA1-939 510 Mathematics. Mathematics. Mathematics, general. ssj0001298528 9780387901121[0387901124](print) 9781461263760[146126376X] 2020.06.27 2020.06.28