Total Separation and Asymptotic Stability
نویسندگان
چکیده
The main goal of this paper is to weaken the invariance assumptions in Liapunov’s direct method. Various geometric conditions resembling those provided by the collection of level surfaces of Liapunov functions are investigated. They are used to derive necessary resp. sufficient conditions for the asymptotic stability of equilibrium points of dynamical systems in Banach spaces. The main result — which does not hold true in the infinite–dimensional setting — is a consequence of the Zubov–Ura–Kimura
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تاریخ انتشار 2004