Impulsive differential inclusions involving evolution operators in separable Banach spaces
We present some results on the existence of mild solutions and study the topological structures of the sets of solutions for the following first-order impulsive semilinear differential inclusions with initial and boundary conditions: where J=R+, 0 = t 0 < t 1 < … < t m <…, m∈N, lim k→∞...
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| Datum: | 2012 |
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| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Український математичний журнал
2012
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| Schriftenreihe: | Український математичний журнал |
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| Online Zugang: | http://dspace.nbuv.gov.ua/handle/123456789/164445 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Impulsive differential inclusions involving evolution operators in separable Banach spaces / M. Benchohra, J.J. Nieto, A. Ouahab // Український математичний журнал. — 2012. — Т. 64, № 7. — С. 867-891. — Бібліогр.: 63 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | We present some results on the existence of mild solutions and study the topological structures of the sets of solutions for the following first-order impulsive semilinear differential inclusions with initial and boundary conditions:
where J=R+, 0 = t 0 < t 1 < … < t m <…, m∈N, lim k→∞ t k = ∞, A(t) is the infinitesimal generator of a family of evolution operators U(t, s) in a separable Banach space E and F is a set-valued mapping. The functions I k characterize the jumps of solutions at the impulse points t k , k = 1, ….The mapping L: PC b →E is a bounded linear operator. We also investigate the compactness of the set of solutions, some regularity properties of the operator solutions, and the absolute retract. |
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