A Variational Approach to Nonsmooth Dynamics by Samir Adly

Author:Samir Adly
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

(ii) ;

(iii) is closed.

Then for any , , the orbit

is bounded and the following asymptotic properties hold

Proof

From the proof of Theorem 4.2.1, we know that the study of our problem reduces to one of the first-order system where A is defined in (4.9) and is defined as in the proof of Theorem 4.2.2. Let us first check that all assumptions of Corollary 3.​3.​1 are satisfied with defined as in the proof of Theorem 4.2.2, i.e. We have and the function is thus lower semicontinuous. It follows that hypothesis (i) of Corollary 3.​3.​1 is satisfied. We have

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