Some averaging results for ordinary differential inclusions

Amel Bourada; Rahma Guen; Mustapha Lakrib; Karim Yadi

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

  • Volume: 35, Issue: 1, page 47-63
  • ISSN: 1509-9407

Abstract

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We consider ordinary differential inclusions and we state and discuss some averaging results for these inclusions. Our results are proved under weaker conditions than the results in the literature.

How to cite

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Amel Bourada, et al. "Some averaging results for ordinary differential inclusions." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 35.1 (2015): 47-63. <http://eudml.org/doc/276646>.

@article{AmelBourada2015,
abstract = {We consider ordinary differential inclusions and we state and discuss some averaging results for these inclusions. Our results are proved under weaker conditions than the results in the literature.},
author = {Amel Bourada, Rahma Guen, Mustapha Lakrib, Karim Yadi},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
keywords = {ordinary differential inclusions; averaging method},
language = {eng},
number = {1},
pages = {47-63},
title = {Some averaging results for ordinary differential inclusions},
url = {http://eudml.org/doc/276646},
volume = {35},
year = {2015},
}

TY - JOUR
AU - Amel Bourada
AU - Rahma Guen
AU - Mustapha Lakrib
AU - Karim Yadi
TI - Some averaging results for ordinary differential inclusions
JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization
PY - 2015
VL - 35
IS - 1
SP - 47
EP - 63
AB - We consider ordinary differential inclusions and we state and discuss some averaging results for these inclusions. Our results are proved under weaker conditions than the results in the literature.
LA - eng
KW - ordinary differential inclusions; averaging method
UR - http://eudml.org/doc/276646
ER -

References

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  1. [1] J.P. Aubin and A. Cellina, Differential Inclusions. Set-Valued Maps and Viability Theory (Springer Verlag, Berlin-Heidelberg-New York-Tokyo, 1984). doi: 10.1007/978-3-642-69512-4 Zbl0538.34007
  2. [2] K. Deimling, Multivalued Differential Equations (Walter de Gruyter, Berlin, 1992). doi: 10.1515/9783110874228 Zbl0760.34002
  3. [3] G. Grammel, Averaging of multivalued differential equations, Int. J. Math. Math. Sci. 25 (2003), 1615-1622. doi: 10.1155/S016117120300680X Zbl1036.34013
  4. [4] S. Hu and N.S. Papageorgiou, Handbook of Multivalued Analysis, Volume I: Theory, Kluwer Academic Publishers (Dordrecht-Boston-London, 1997). Zbl0887.47001
  5. [5] T. Janiak and E. Łuczak-Kumorek, Method of averaging for the system of functional-differential inclusions, Discuss. Math. 16 (1996), 137-151. Zbl0910.34058
  6. [6] T. Janiak and E. Łuczak-Kumorek, Averaging of neutral inclusions when the average value of the right-hand side does not exist, Acta Math. Viet. 25 (2000), 1-11. Zbl0954.34039
  7. [7] S. Klymchuk, A. Plotnikov and N. Skripnik, Overview of V.A. Plotnikov's research on averaging of differential inclusions, Physica D: Nonlinear Phenomena 241 (2012), 1932-1947. doi: 10.1016/j.physd.2011.05.004 
  8. [8] N.A. Perestyuk, V.A. Plotnikov, A.M. Samoilenko and N.V. Skripnik, Differential equations with impulse effects: multivalued right-hand sides with discontinuities, (De Gruyter Studies in Mathematics: 40). Berlin/Boston: Walter De Gruyter GmbH&Co., 2011. Zbl1234.34002
  9. [9] N.V. Plotnikova, The Krasnosel'skii-Krein theorem for differential inclusions, Differ. Eq. 41 (2005), 1049-1053. doi: 10.1007/s10625-005-0248-5 Zbl1109.34306
  10. [10] G.V. Smirnov, Introduction to the Theory of Differential Inclusions, Graduate Studies in Math. 41, AMS, Providence, 2002. 

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