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Near viability for fully nonlinear differential inclusions

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Central European Journal of Mathematics

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.

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Authors and Affiliations

  1. Department of Mathematics, “Al. I. Cuza” University of Iaşi, Bd. Carol I, no. 11, Iaşi, 700506, Romania

    Irina Căpraru & Alina I. Lazu

  2. Department of Mathematics, “Gh. Asachi” Technical University, Iaşi, 700506, Romania

    Alina I. Lazu

Authors
  1. Irina Căpraru
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  2. Alina I. Lazu
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Correspondence to Irina Căpraru.

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Căpraru, I., Lazu, A.I. Near viability for fully nonlinear differential inclusions. centr.eur.j.math. 12, 1447–1459 (2014). https://doi.org/10.2478/s11533-014-0424-z

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  • DOI: https://doi.org/10.2478/s11533-014-0424-z

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