Filippov Lemma for certain second order differential inclusions

• Autorzy: Grzegorz Bartuzel , Andrzej Fryszkowski
• Języki publikacji: EN

Abstrakty

EN

In the paper we give an analogue of the Filippov Lemma for the second order differential inclusions with the initial conditions y(0) = 0, y′(0) = 0, where the matrix A ∈ ℝd×d and multifunction is Lipschitz continuous in y with a t-independent constant l. The main result is the following: Assume that F is measurable in t and integrably bounded. Let y 0 ∈ W 2,1 be an arbitrary function fulfilling the above initial conditions and such that where p 0 ∈ L 1[0, 1]. Then there exists a solution y ∈ W 2,1 to the above differential inclusions such that a.e. in [0, 1], .

Słowa kluczowe

EN

Differential inclusion; Differential operator; Lipschitz multifunction; Filippov Lemma

Kategorie tematyczne

• 39A05: General theory
• 26A24: Differentiation (functions of one variable): general theory, generalized derivatives, mean-value theorems
• 46G05: Derivatives
• 28A15: Abstract differentiation theory, differentiation of set functions
• 28A05: Classes of sets (Borel fields, σ -rings, etc.), measurable sets, Suslin sets, analytic sets

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2012
• Tom: 10
• Numer: 6
• Strony: 1944-1952

Daty

wydano

2012-12-01

online

2012-10-12

Twórcy

autor

Grzegorz Bartuzel

• Faculty of Mathematics and Information Science, Warsaw University of Technology, Koszykowa 75, 00-662, Warsaw, Poland

autor

Andrzej Fryszkowski

• Faculty of Mathematics and Information Science, Warsaw University of Technology, Koszykowa 75, 00-662, Warsaw, Poland

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-012-0119-2