On the theorem of Filippov-Pliś and some applications

• Autorzy: Donchev T. , Farkhi E.
• Języki publikacji: EN

Abstrakty

EN

In the paper some known and new extensions of the famous theorem of Filippov (1967) and a theorem of Plis (1965) for differential inclusions are presented. We replace the Lipschitz condition on the set-valued map in the right-hand side by a weaker onesided Lipschitz (OSL), one-sided Kamke (OSK) or a continuity-like condition (CLC). We prove new Filippov-type theorems for singularly perturbed and evolution inclusions with OSL right-hand sides. In the CLC case we obtain two extended theorems, one of which implies directly the relaxation theorem. We obtain also a theorem in Banach spaces for OSK multifunctions. Some applications to exponential formulae are surveyed.

Słowa kluczowe

EN

differential inclusions; one-sided; Lipschitz; Filippov; Plis

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2009
• Tom: Vol. 38, no 4A
• Strony: 1251--1271
• Opis fizyczny: Bibliogr. 33 poz.

Twórcy

autor

Donchev T.

autor

Farkhi E.

• Department of Mathematics, University of Architecture & Civil Engineering, 1046 Sofia, Bulgaria,

Bibliografia

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