# Filippov Lemma for certain second order differential inclusions

Grzegorz Bartuzel; Andrzej Fryszkowski

Open Mathematics (2012)

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

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topGrzegorz 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 -

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