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Open Mathematics

formerly Central European Journal of Mathematics

Editor-in-Chief: Gianazza, Ugo / Vespri, Vincenzo

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Volume 12, Issue 10

Issues

Volume 13 (2015)

Near viability for fully nonlinear differential inclusions

Irina Căpraru / Alina Lazu
  • Department of Mathematics, “Al. I. Cuza” University of Iaşi, Bd. Carol I, no. 11, Iaşi, 700506, Romania
  • Department of Mathematics, “Gh. Asachi” Technical University, Iaşi, 700506, Romania
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Published Online: 2014-06-21 | DOI: https://doi.org/10.2478/s11533-014-0424-z

Abstract

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.

MSC: 34G20; 47J35

Keywords: Nonlinear differential inclusions; A priori estimates; Near viability

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About the article

Published Online: 2014-06-21

Published in Print: 2014-10-01


Citation Information: Open Mathematics, Volume 12, Issue 10, Pages 1447–1459, ISSN (Online) 2391-5455, DOI: https://doi.org/10.2478/s11533-014-0424-z.

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