Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

Generalization of the Lyapunov Theorem On Conditional Stability for Nonanalytic Case

Author(s):

Sergey G. Kryzhevich

198904, Russia, Saint-Petersburg, Bibliotechnaja sq. 2,
Saint-Petersburg State University
Mathematics and Mechanics Faculty

Abstract:

We consider a smooth system of ordinary differential equations in a neighborhood of a trivial solution. A system is assumed to have first derivatives with respect to phase variables. The Jacobi matrix is assumed to be H\"ol\-der continuous. We show that the well-known Lyapunov theorem on conditional stability remains valid for such systems.

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