# Multivalued linear operators and differential inclusions in Banach spaces

Anatolii Baskakov; Valeri Obukhovskii; Pietro Zecca

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (2003)

- Volume: 23, Issue: 1, page 53-74
- ISSN: 1509-9407

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topAnatolii Baskakov, Valeri Obukhovskii, and Pietro Zecca. "Multivalued linear operators and differential inclusions in Banach spaces." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 23.1 (2003): 53-74. <http://eudml.org/doc/271435>.

@article{AnatoliiBaskakov2003,

abstract = {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.},

author = {Anatolii Baskakov, Valeri Obukhovskii, Pietro Zecca},

journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},

keywords = {multivalued linear operator; generalized semigroup; minimal growth at infinity; Hille-Yosida condition; degenerate differential inclusion; Cauchy problem; bounded solution; differential inclusion},

language = {eng},

number = {1},

pages = {53-74},

title = {Multivalued linear operators and differential inclusions in Banach spaces},

url = {http://eudml.org/doc/271435},

volume = {23},

year = {2003},

}

TY - JOUR

AU - Anatolii Baskakov

AU - Valeri Obukhovskii

AU - Pietro Zecca

TI - Multivalued linear operators and differential inclusions in Banach spaces

JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization

PY - 2003

VL - 23

IS - 1

SP - 53

EP - 74

AB - 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.

LA - eng

KW - multivalued linear operator; generalized semigroup; minimal growth at infinity; Hille-Yosida condition; degenerate differential inclusion; Cauchy problem; bounded solution; differential inclusion

UR - http://eudml.org/doc/271435

ER -

## References

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- [10] V. Obukhovskii and P. Zecca, On boundary value problems for degenerate differential inclusions in Banach spaces, Abstr. Appl. Anal. 13 (2003), 769-784. Zbl1076.34070
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