Geodesic
Multivalued linear operators and differential inclusions in Banach spaces
Discussiones Mathematicae. Differential Inclusions, Control and Optimization, Tome 23 (2003) no. 1, pp. 53-74.

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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.
Keywords: multivalued linear operator, generalized semigroup, minimal growth at infinity, Hille-Yosida condition, degenerate differential inclusion, Cauchy problem, bounded solution 
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Baskakov, Anatolii; Obukhovskii, Valeri; Zecca, Pietro. Multivalued linear operators and differential inclusions in Banach spaces. Discussiones Mathematicae. Differential Inclusions, Control and Optimization, Tome 23 (2003) no. 1, pp. 53-74. http://geodesic.mathdoc.fr/item/DMDICO_2003_23_1_a4/

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