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Approximate weak invariance for semilinear differential inclusions in Banach spaces

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Lazu A., Postolache V.

Open Mathematics

2011

tom 9

nr 5

1143-1155

In this paper we give a criterion for a given set K in Banach space to be approximately weakly invariant with respect to the differential inclusion x′(t) ∈ Ax(t) + F(x(t)), where A generates a C 0-semigroup and F is a given multi-function, using the concept of a tangent set to another set. As an application, we establish the relation between approximate solutions to the considered differential inclusion and solutions to the relaxed one, i.e., x′(t) ∈ Ax(t) + $\overline {co} $ F(x(t)), without any Lipschitz conditions on the multi-function F.

Ograniczanie wyników

1 Open Mathematics

1 Lazu A.

1 Postolache V.

1 2011

Wyniki wyszukiwania

Approximate weak invariance for semilinear differential inclusions in Banach spaces