Controllability for some partial functional integrodifferential equations with nonlocal conditions in Banach spaces

Khalil Ezzinbi; Guy Degla; Patrice Ndambomve

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (2015)

  • Volume: 35, Issue: 1, page 25-46
  • ISSN: 1509-9407

Abstract

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This work concerns the study of the controllability of some partial functional integrodifferential equation with nonlocal initial conditions in Banach spaces. It gives sufficient conditions that ensure the controllability of the system by supposing that its linear homogeneous part admits a resolvent operator in the sense of Grimmer, and by making use of the measure of noncompactness and the Mönch fixed-point theorem. As a result, we obtain a generalization of the work of Y.K. Chang, J.J. Nieto and W.S. Li (J. Optim. Theory Appl. 142, 267-273 (2009)), without assuming the compactness of the resolvent operator. An example of application is given for illustration.

How to cite

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Khalil Ezzinbi, Guy Degla, and Patrice Ndambomve. "Controllability for some partial functional integrodifferential equations with nonlocal conditions in Banach spaces." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 35.1 (2015): 25-46. <http://eudml.org/doc/276608>.

@article{KhalilEzzinbi2015,
abstract = {This work concerns the study of the controllability of some partial functional integrodifferential equation with nonlocal initial conditions in Banach spaces. It gives sufficient conditions that ensure the controllability of the system by supposing that its linear homogeneous part admits a resolvent operator in the sense of Grimmer, and by making use of the measure of noncompactness and the Mönch fixed-point theorem. As a result, we obtain a generalization of the work of Y.K. Chang, J.J. Nieto and W.S. Li (J. Optim. Theory Appl. 142, 267-273 (2009)), without assuming the compactness of the resolvent operator. An example of application is given for illustration.},
author = {Khalil Ezzinbi, Guy Degla, Patrice Ndambomve},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
keywords = {controllability; integrodifferential equations; nonlocal initial condition; resolvent operator; Mönch fixed-point theorem},
language = {eng},
number = {1},
pages = {25-46},
title = {Controllability for some partial functional integrodifferential equations with nonlocal conditions in Banach spaces},
url = {http://eudml.org/doc/276608},
volume = {35},
year = {2015},
}

TY - JOUR
AU - Khalil Ezzinbi
AU - Guy Degla
AU - Patrice Ndambomve
TI - Controllability for some partial functional integrodifferential equations with nonlocal conditions in Banach spaces
JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization
PY - 2015
VL - 35
IS - 1
SP - 25
EP - 46
AB - This work concerns the study of the controllability of some partial functional integrodifferential equation with nonlocal initial conditions in Banach spaces. It gives sufficient conditions that ensure the controllability of the system by supposing that its linear homogeneous part admits a resolvent operator in the sense of Grimmer, and by making use of the measure of noncompactness and the Mönch fixed-point theorem. As a result, we obtain a generalization of the work of Y.K. Chang, J.J. Nieto and W.S. Li (J. Optim. Theory Appl. 142, 267-273 (2009)), without assuming the compactness of the resolvent operator. An example of application is given for illustration.
LA - eng
KW - controllability; integrodifferential equations; nonlocal initial condition; resolvent operator; Mönch fixed-point theorem
UR - http://eudml.org/doc/276608
ER -

References

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