# Filippov Lemma for certain second order differential inclusions

Open Mathematics (2012)

• Volume: 10, Issue: 6, page 1944-1952
• ISSN: 2391-5455

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## Abstract

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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], .

## How to cite

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Grzegorz Bartuzel, and Andrzej Fryszkowski. "Filippov Lemma for certain second order differential inclusions." Open Mathematics 10.6 (2012): 1944-1952. <http://eudml.org/doc/269058>.

@article{GrzegorzBartuzel2012,
abstract = {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], .},
author = {Grzegorz Bartuzel, Andrzej Fryszkowski},
journal = {Open Mathematics},
keywords = {Differential inclusion; Differential operator; Lipschitz multifunction; Filippov Lemma; differential inclusion; differential operator; Filippov lemma},
language = {eng},
number = {6},
pages = {1944-1952},
title = {Filippov Lemma for certain second order differential inclusions},
url = {http://eudml.org/doc/269058},
volume = {10},
year = {2012},
}

TY - JOUR
AU - Grzegorz Bartuzel
AU - Andrzej Fryszkowski
TI - Filippov Lemma for certain second order differential inclusions
JO - Open Mathematics
PY - 2012
VL - 10
IS - 6
SP - 1944
EP - 1952
AB - 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], .
LA - eng
KW - Differential inclusion; Differential operator; Lipschitz multifunction; Filippov Lemma; differential inclusion; differential operator; Filippov lemma
UR - http://eudml.org/doc/269058
ER -

## References

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