We consider the nonlinear differential inclusion x′(t) ∈ Ax(t) + F(x(t)), where A is an m-dissipative operator on a separable Banach space X and F is a multi-function. We establish a viability result under Lipschitz hypothesis on F, that consists in proving the existence of solutions of the differential inclusion above, starting from a given set, which remain arbitrarily close to that set, if a tangency condition holds. To this end, we establish a kind of set-valued Gronwall’s lemma and a compactness theorem, which are extensions to the nonlinear case of similar results for semilinear differential inclusions. As an application, we give an approximate null controllability result.
@article{bwmeta1.element.doi-10_2478_s11533-014-0424-z,
author = {Irina C\u apraru and Alina Lazu},
title = {Near viability for fully nonlinear differential inclusions},
journal = {Open Mathematics},
volume = {12},
year = {2014},
pages = {1447-1459},
zbl = {1307.34095},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-014-0424-z}
}
Irina Căpraru; Alina Lazu. Near viability for fully nonlinear differential inclusions. Open Mathematics, Tome 12 (2014) pp. 1447-1459. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-014-0424-z/
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