Controllability for impulsive semilinear functional differential inclusions with a non-compact evolution operator

• Autorzy: Irene Benedetti , Valeri Obukhovskii , Pietro Zecca
• Języki publikacji: EN

Abstrakty

EN

We study a controllability problem for a system governed by a semilinear functional differential inclusion in a Banach space in the presence of impulse effects and delay. Assuming a regularity of the multivalued non-linearity in terms of the Hausdorff measure of noncompactness we do not require the compactness of the evolution operator generated by the linear part of inclusion. We find existence results for mild solutions of this problem under various growth conditions on the nonlinear part and on the jump functions. As example, we consider the controllability of an impulsive system governed by a wave equation with delayed feedback.

Słowa kluczowe

EN

evolution differential inclusion; impulsive inclusion; control system; controllability; mild solution; condensing multimap; fixed point

Kategorie tematyczne

• 47H08: Measures of noncompactness and condensing mappings, K -set contractions, etc.
• 47H04: Set-valued operators
• 34K45: Equations with impulses
• 34K09: Functional-differential inclusions
• 47H11: Degree theory
• 34G25: Evolution inclusions
• 47H10: Fixed-point theorems
• 93B05: Controllability

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae, Differential Inclusions, Control and Optimization
• Rocznik: 2011
• Tom: 31
• Numer: 1
• Strony: 39-69

Daty

wydano

2011

otrzymano

2009-12-30

Twórcy

autor

Irene Benedetti

• Università degli Studi di Firenze, Dipartimento di Energetica "S. Stecco", via S. Marta 3-1, 50139 Firenze, Italia

autor

Valeri Obukhovskii

• Voronezh State University, Faculty of Mathematics, Universitetskaya pl. 1, 394006 Voronezh, Russia

autor

Pietro Zecca

• Università degli Studi di Firenze, Dipartimento di Energetica "S. Stecco", via S. Marta 3-1, 50139 Firenze, Italia

Bibliografia

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Identyfikatory

DOI

10.7151/dmdico.1127