Open AccessA metric proof of the converse Lyapunov theorem for semicontinuous multivalued dynamics
Author(s) -
Gabriele Terrone,
Antonio Siconolfi
Publication year - 2012
Publication title -
discrete and continuous dynamical systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.289
H-Index - 70
eISSN - 1553-5231
pISSN - 1078-0947
DOI - 10.3934/dcds.2012.32.4409
Subject(s) - converse , mathematics , lyapunov function , metric (unit) , vector field , metric space , fixed point theorem , pure mathematics , ordinary differential equation , kolmogorov–arnold–moser theorem , mathematical analysis , differential equation , hamiltonian system , nonlinear system , physics , operations management , geometry , quantum mechanics , economics
International audienceWe extend the metric proof of the inverse Lyapunov Theorem, given in [13] for continuous multivalued dynamics, by means of tools issued from weak KAMtheory, to the case where the set-valued vector field is just upper semicontinuous. This generality is justified especially in view of application to discontinuous ordinary differential equations. The more relevant new point is that we introduce, to compensate the lack of continuity, a family of perturbed dynamics, obtained through internal approximation of the original one, and perform some stability analysis of it
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