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Multivalued linear operators and differential inclusions in Banach spaces

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Baskakov A., Obukhovskii V., Zecca P.

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

2003

tom 23

nr 1

53-74

In this paper, we study multivalued linear operators (MLO's) and their resolvents in non reflexive Banach spaces, introducing a new condition of a minimal growth at infinity, more general than the Hille-Yosida condition. Then we describe the generalized semigroups induced by MLO's. We present a criterion for an MLO to be a generator of a generalized semigroup in an arbitrary Banach space. Finally, we obtain some existence results for differential inclusions with MLO's and various types of multivalued nonlinearities. As a consequence, we give theorems on the existence of local, global and bounded solutions of the Cauchy problem for degenerate differential inclusions.

Ograniczanie wyników

1 Discussiones Mathematicae, Differential Inclusions, Control and Optimization

1 Baskakov A.

1 Obukhovskii V.

1 Zecca P.

1 2003

Wyniki wyszukiwania

Multivalued linear operators and differential inclusions in Banach spaces