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Near viability for fully nonlinear differential inclusions

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Căpraru I., Lazu A.

Open Mathematics

2014

tom 12

nr 10

1447-1459

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.

Ograniczanie wyników

1 Open Mathematics

1 Căpraru I.

1 Lazu A.

1 2014

Wyniki wyszukiwania

Near viability for fully nonlinear differential inclusions