Stability of periodic solutions for Lipschitz systems obtained via the averaging method

Buică, Adriana; Daniilidis, Aris

doi:10.1090/S0002-9939-07-08929-0

Stability of periodic solutions for Lipschitz systems obtained via the averaging method
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by Adriana Buică and Aris Daniilidis PDF

Proc. Amer. Math. Soc. 135 (2007), 3317-3327 Request permission

Abstract:

Existence and asymptotic stability of the periodic solutions of the Lipschitz system $x’ (t)=\varepsilon F(t,x,\varepsilon )$ is hereby studied via the averaging method. The traditional $C^{1}$ dependence of $F(s,\cdot ,\varepsilon )$ on $z$ is relaxed to the mere strict differentiability of $F(s,\cdot ,0)$ at $z=z_{0}$ for $\varepsilon =0$, giving room to potential applications for structured nonsmooth systems.

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