Asymptotically autonomous semiflows: chain recurrence and Lyapunov functions

作者: Konstantin Mischaikow , Hal Smith , Horst R. Thieme

DOI: 10.1090/S0002-9947-1995-1290727-7

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摘要: From the work of C. Conley, it is known that omega limit set a precompact orbit an autonomous semiflow chain recurrent set. Here, we improve result L. Markus by showing solution asymptotically relative to limiting semiflow. In special case there Lyapunov function for semiflow, sufficient conditions are given be contained in level function.

参考文章(21)
JOSEPH P. LASALLE, Stability Theory and Invariance Principles Dynamical Systems#R##N#An International Symposium, Volume 1. pp. 211- 222 ,(1976) , 10.1016/B978-0-12-164901-2.50021-0
Charles Conley, Isolated Invariant Sets and the Morse Index American Mathematical Society. ,vol. 38, ,(1978) , 10.1090/CBMS/038
Viktor Vladimirovich Nemytskii, Qualitative theory of differential equations ,(1960)
Jack K. Hale, Sjoerd M. Verduyn Lunel, Introduction to Functional Differential Equations ,(1993)
Ray Redheffer, Jack K. Hale, Ordinary differential equations American Mathematical Monthly. ,vol. 78, pp. 1154- ,(1971) , 10.2307/2316346
George R. Sell, NONAUTONOMOUS DIFFERENTIAL EQUATIONS AND TOPOLOGICAL DYNAMICS. I. THE BASIC THEORY Transactions of the American Mathematical Society. ,vol. 127, pp. 241- 262 ,(1967) , 10.1090/S0002-9947-1967-0212313-2
John E. Franke, James F. Selgrade, Abstract -limit sets, chain recurrent sets, and basic sets for flows Proceedings of the American Mathematical Society. ,vol. 60, pp. 309- 316 ,(1976) , 10.1090/S0002-9939-1976-0423423-X