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

Irene Benedetti; Valeri Obukhovskii; Pietro Zecca

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (2011)

  • Volume: 31, Issue: 1, page 39-69
  • ISSN: 1509-9407

Abstract

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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.

How to cite

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Irene Benedetti, Valeri Obukhovskii, and Pietro Zecca. "Controllability for impulsive semilinear functional differential inclusions with a non-compact evolution operator." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 31.1 (2011): 39-69. <http://eudml.org/doc/271185>.

@article{IreneBenedetti2011,
abstract = {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.},
author = {Irene Benedetti, Valeri Obukhovskii, Pietro Zecca},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
keywords = {evolution differential inclusion; impulsive inclusion; control system; controllability; mild solution; condensing multimap; fixed point; fixed-point; impulsive semilinear functional differential inclusions; noncompact evolution operator; wave equation; impulsive semilinear functional differential inclusions; non-compact evolution operator; wave equation; jump functions; Hausdorff measure; multivalued nonlinearity},
language = {eng},
number = {1},
pages = {39-69},
title = {Controllability for impulsive semilinear functional differential inclusions with a non-compact evolution operator},
url = {http://eudml.org/doc/271185},
volume = {31},
year = {2011},
}

TY - JOUR
AU - Irene Benedetti
AU - Valeri Obukhovskii
AU - Pietro Zecca
TI - Controllability for impulsive semilinear functional differential inclusions with a non-compact evolution operator
JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization
PY - 2011
VL - 31
IS - 1
SP - 39
EP - 69
AB - 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.
LA - eng
KW - evolution differential inclusion; impulsive inclusion; control system; controllability; mild solution; condensing multimap; fixed point; fixed-point; impulsive semilinear functional differential inclusions; noncompact evolution operator; wave equation; impulsive semilinear functional differential inclusions; non-compact evolution operator; wave equation; jump functions; Hausdorff measure; multivalued nonlinearity
UR - http://eudml.org/doc/271185
ER -

References

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