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On the uniqueness of solutions to a class of discontinuous dynamical systems

Domenii publicaţii > Matematica + Tipuri publicaţii > Articol în revistã ştiinţificã

Autori: Marius-F. Danca

Editorial: Elsevier, Nonlinear Analysis Series B: Real World Applications, 11, p.1402-1412, 2010.


The study of uniqueness of solutions of discontinuous dynamical systems has an important implication: multiple solutions to the initial value problem could not be found in such real dynamical systems; the (attracting or repulsive) sliding mode is inherently linked to the uniqueness of solutions. In this paper a strengthened Lipschitz-like condition for di¤erential inclusions and a geometrical approach for the uniqueness of solutions for a class of Filippov dynamical systems are presented. Several theoretical and practical examples are discussed.

Cuvinte cheie: Filippov solutions, attractive sliding mode, repulsive sliding mode, strengthened one side Lipschitz condition