Delay perturbed evolution problems involving time dependent subdifferential operators

Soumia Saïdi; Mustapha Fateh Yarou

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (2014)

  • Volume: 34, Issue: 1, page 61-87
  • ISSN: 1509-9407

Abstract

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We investigate in the present paper, the existence and uniqueness of solutions for functional differential inclusions involving a subdifferential operator in the infinite dimensional setting. The perturbation which contains the delay is single-valued, separately measurable, and separately Lipschitz. We prove, without any compactness condition, that the problem has one and only one solution.

How to cite

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Soumia Saïdi, and Mustapha Fateh Yarou. "Delay perturbed evolution problems involving time dependent subdifferential operators." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 34.1 (2014): 61-87. <http://eudml.org/doc/270614>.

@article{SoumiaSaïdi2014,
abstract = {We investigate in the present paper, the existence and uniqueness of solutions for functional differential inclusions involving a subdifferential operator in the infinite dimensional setting. The perturbation which contains the delay is single-valued, separately measurable, and separately Lipschitz. We prove, without any compactness condition, that the problem has one and only one solution.},
author = {Soumia Saïdi, Mustapha Fateh Yarou},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
keywords = {Differential inclusions; subdifferential operator; Lipschitz functions; set-valued map; delay; perturbation; absolutely continuous map; differential inclusions},
language = {eng},
number = {1},
pages = {61-87},
title = {Delay perturbed evolution problems involving time dependent subdifferential operators},
url = {http://eudml.org/doc/270614},
volume = {34},
year = {2014},
}

TY - JOUR
AU - Soumia Saïdi
AU - Mustapha Fateh Yarou
TI - Delay perturbed evolution problems involving time dependent subdifferential operators
JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization
PY - 2014
VL - 34
IS - 1
SP - 61
EP - 87
AB - We investigate in the present paper, the existence and uniqueness of solutions for functional differential inclusions involving a subdifferential operator in the infinite dimensional setting. The perturbation which contains the delay is single-valued, separately measurable, and separately Lipschitz. We prove, without any compactness condition, that the problem has one and only one solution.
LA - eng
KW - Differential inclusions; subdifferential operator; Lipschitz functions; set-valued map; delay; perturbation; absolutely continuous map; differential inclusions
UR - http://eudml.org/doc/270614
ER -

References

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  10. [10] J.F. Edmond, Delay perturbed sweeping process, Set-Valued Anal. 14 (2006) 295-317. doi: 10.1007/s11228-006-0021-9 Zbl1122.34060
  11. [11] E. Mitidieri and I. Vrabie, Existence for nonlinear functional differential equations, Hiroshima Math. J. 17 (1987) 627-649. Zbl0655.34055
  12. [12] M. Kisielewicz, Differential Inclusions and Optimal Control (Kluwer, Dordrecht, The Netherlands, 1991). 
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  14. [14] S. Saïdi, L. Thibault and M. Yarou, Relaxation of optimal control problems involving time dependent subdifferential operators, Numerical Funct. Anal. Optimization 34 (10) (2013) 1156-1186. doi: 10.1080/01630563.2013.807287 Zbl1288.34057

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