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.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1046,
author = {Anatolii Baskakov and Valeri Obukhovskii and Pietro Zecca},
title = {Multivalued linear operators and differential inclusions in Banach spaces},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
volume = {23},
year = {2003},
pages = {53-74},
zbl = {1059.34036},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1046}
}
Anatolii Baskakov; Valeri Obukhovskii; Pietro Zecca. Multivalued linear operators and differential inclusions in Banach spaces. Discussiones Mathematicae, Differential Inclusions, Control and Optimization, Tome 23 (2003) pp. 53-74. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1046/
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