We prove the existence of at least one integrated solution to an impulsive Cauchy problem for an integro-differential inclusion in a Banach space with a non-densely defined operator. Since we look for integrated solution we do not need to assume that A is a Hille Yosida operator. We exploit a technique based on the measure of weak non-compactness which allows us to avoid any hypotheses of compactness both on the semigroup generated by the linear part and on the nonlinear term. As the main tool in the proof of our existence result, we are using the Glicksberg–Ky Fan theorem on a fixed point for a multivalued map on a compact convex subset of a locally convex topological vector space.

On solvability of the impulsive Cauchy problem for integro-differential inclusions with non-densely defined operators / Benedetti, Irene; Obukhovskii, Valeri; Taddei, Valentina. - In: PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY OF LONDON SERIES A: MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES. - ISSN 1364-503X. - 379:2191(2021), pp. 1-15. [10.1098/rsta.2019.0384]

On solvability of the impulsive Cauchy problem for integro-differential inclusions with non-densely defined operators

Valeri Obukhovskii
;
Valentina Taddei
2021

Abstract

We prove the existence of at least one integrated solution to an impulsive Cauchy problem for an integro-differential inclusion in a Banach space with a non-densely defined operator. Since we look for integrated solution we do not need to assume that A is a Hille Yosida operator. We exploit a technique based on the measure of weak non-compactness which allows us to avoid any hypotheses of compactness both on the semigroup generated by the linear part and on the nonlinear term. As the main tool in the proof of our existence result, we are using the Glicksberg–Ky Fan theorem on a fixed point for a multivalued map on a compact convex subset of a locally convex topological vector space.
4-gen-2021
379
2191
1
15
On solvability of the impulsive Cauchy problem for integro-differential inclusions with non-densely defined operators / Benedetti, Irene; Obukhovskii, Valeri; Taddei, Valentina. - In: PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY OF LONDON SERIES A: MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES. - ISSN 1364-503X. - 379:2191(2021), pp. 1-15. [10.1098/rsta.2019.0384]
Benedetti, Irene; Obukhovskii, Valeri; Taddei, Valentina
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/1225996
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