Necessary and sufficient conditions for the existence of equilibrium in abstract non-autonomous functional differential equations  

作　　者：ZHENG ZuoHuan 1 & LI XiLiang 2 1 Institute of Applied Mathematics,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China 2 College of Mathematics and Information Sciences,Shandong Institute of Business and Technology,Yantai 264005,ChinaAbstract In this article,we aim to establish necessary and sufficient conditions that guarantee the existence of equilibria and continuous equilibria for the continuous skew-product semiflow induced by a class of 

出　　处：《Science China Mathematics》2010年第8期2045-2059,共15页中国科学：数学（英文版）

基　　金：supported by the Key Lab of Random Complex Structures and Data Science,CAS(Grant No.2008DP173182);the National Basic Research Program of China (973 Project)(Grant No.2005CB321902)

摘　　要：non-autonomous finite-delay functional differential equations without any monotone conditions assumed.A minimal set is constructed in terms of which necessary and sufficient conditions for a continuous equilibrium to exist are also obtained.Several illustrative examples are employed to demonstrate our results.non-autonomous finite-delay functional differential equations without any monotone conditions assumed.A minimal set is constructed in terms of which necessary and sufficient conditions for a continuous equilibrium to exist are also obtained.Several illustrative examples are employed to demonstrate our results.

关 键 词：continuous EQUILIBRIUM NON-AUTONOMOUS functional differential equations skew-product SEMIFLOWS TOPOLOGICAL dynamics 

分 类 号：O175[理学—数学]