Set-Valued and Variational Analysis

, Volume 23, Issue 3, pp 559–575 | Cite as

On the Lipschitz Behavior of Solution Maps of a Class of Differential Inclusions

  • Lukáš Adam


We consider a general differential inclusion which is parameterized by a parameter. We perform time discretization and present conditions under which the discretized solution map is locally Lipschitz. Further, if the Lipschitzian modulus is bounded in some sense, we show that it is possible to obtain the local Lipschitzian property even for the original (not discretized) solution map. We conclude the paper with an example concerning stability analysis of nonregular electrical circuits with ideal diodes.


Differential inclusions Lipschitzian continuity Stability Variational analysis Electrical circuits 

Mathematics Subject Classification (2010)

34A60 34H05 49K21 34A36 


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© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Institute of Information Theory and Automation, Czech Academy of SciencesPrague 8Czech Republic

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