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], .
@article{bwmeta1.element.doi-10_2478_s11533-012-0119-2,
author = {Grzegorz Bartuzel and Andrzej Fryszkowski},
title = {Filippov Lemma for certain second order differential inclusions},
journal = {Open Mathematics},
volume = {10},
year = {2012},
pages = {1944-1952},
zbl = {1268.34044},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0119-2}
}
Grzegorz Bartuzel; Andrzej Fryszkowski. Filippov Lemma for certain second order differential inclusions. Open Mathematics, Tome 10 (2012) pp. 1944-1952. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0119-2/
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