On the averaging of differential inclusions with maxima

Bachir Bar

Mathematica Bohemica (2023)

  • Volume: 148, Issue: 1, page 1-10
  • ISSN: 0862-7959

Abstract

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We apply the averaging method to ordinary differential inclusions with maxima perturbed by a small parameter and illustrate the method by some examples.

How to cite

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Bar, Bachir. "On the averaging of differential inclusions with maxima." Mathematica Bohemica 148.1 (2023): 1-10. <http://eudml.org/doc/299537>.

@article{Bar2023,
abstract = {We apply the averaging method to ordinary differential inclusions with maxima perturbed by a small parameter and illustrate the method by some examples.},
author = {Bar, Bachir},
journal = {Mathematica Bohemica},
keywords = {differential inclusion; maxima; averaging},
language = {eng},
number = {1},
pages = {1-10},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the averaging of differential inclusions with maxima},
url = {http://eudml.org/doc/299537},
volume = {148},
year = {2023},
}

TY - JOUR
AU - Bar, Bachir
TI - On the averaging of differential inclusions with maxima
JO - Mathematica Bohemica
PY - 2023
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 148
IS - 1
SP - 1
EP - 10
AB - We apply the averaging method to ordinary differential inclusions with maxima perturbed by a small parameter and illustrate the method by some examples.
LA - eng
KW - differential inclusion; maxima; averaging
UR - http://eudml.org/doc/299537
ER -

References

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  1. Aubin, J.-P., Cellina, A., Differential Inclusions: Set-Valued Maps and Viability Theory, Grundlehren der Mathematischen Wissenschaften 264. Springer, Berlin (1984),9999DOI99999 10.1007/978-3-642-69512-4 . (1984) Zbl0538.34007MR0755330
  2. Aubin, J.-P., Frankowska, H., Set-Valued Analysis, Systems and Control: Foundations and Applications 2. Birkhäuser, Boston (1990),9999DOI99999 10.1007/978-0-8176-4848-0 . (1990) Zbl0713.49021MR1048347
  3. Aumann, R. J., 10.1016/0022-247X(65)90049-1, J. Math. Anal. Appl. 12 (1965), 1-12. (1965) Zbl0163.06301MR0185073DOI10.1016/0022-247X(65)90049-1
  4. Bainov, D. D., Hristova, S. G., Differential Equations with Maxima, Pure and Applied Mathematics (Boca Raton) 298. CRC Press, Boca Raton (2011),9999DOI99999 10.1201/b10877 . (2011) Zbl1244.34001
  5. Bar, B., Lakrib, M., Averaging method for ordinary differential inclusions with maxima, Electron. J. Differ. Equ. 2018 (2018), Article ID 115, 12 pages 9999MR99999 3831861 . (2018) Zbl1393.34070MR3831861
  6. Bourada, A., Guen, R., Lakrib, M., Yadi, K., 10.7151/dmdico.1169, Discuss. Math., Differ. Incl. Control Optim. 35 (2015), 47-63. (2015) MR3444879DOI10.7151/dmdico.1169
  7. Deimling, K., Multivalued Differential Equations, De Gruyter Series in Nonlinear Analysis and Applications 1. Walter de Gruyter, Berlin (1992),9999DOI99999 10.1515/9783110874228 . (1992) Zbl0760.34002MR1189795
  8. Gama, R., Smirnov, G., 10.1007/s11228-013-0261-4, Set-Valued Var. Anal. 22 (2014), 349-374. (2014) Zbl1307.34001MR3207744DOI10.1007/s11228-013-0261-4
  9. Kichmarenko, O. D., Averaging of differential equations with Hukuhara derivative with maxima, Int. J. Pure Appl. Math. 57 (2009), 447-457. (2009) Zbl1190.34099MR2584470
  10. Kichmarenko, O. D., Sapozhnikova, K. Y., 10.18532/caam.88723, Contemp. Anal. Appl. Math. 3 (2015), 113-122. (2015) Zbl1353.34095MR3333779DOI10.18532/caam.88723
  11. Klymchuk, S., Plotnikov, A., Skripnik, N., 10.1016/j.physd.2011.05.004, Phys. D 241 (2012), 1932-1947. (2012) MR2994333DOI10.1016/j.physd.2011.05.004
  12. Lakrib, M., 10.36045/bbms/1235574188, Bull. Belg. Math. Soc. - Simon. Stevin 16 (2009), 13-29. (2009) Zbl1166.34024MR2498955DOI10.36045/bbms/1235574188
  13. Plotnikov, V. A., Kichmarenko, O. D., Averaging of differential equations with maxima, Nauk. Visn. Chernivets’kogo Univ., Mat. 150 (2002), 78-82 Ukrainian 9999ZBL99999 1071.34519 . (2002) 
  14. Plotnikov, V. A., Kichmarenko, O. D., A note on the averaging method for differential equations with maxima, Iranian J. Optim. 1 (2009), 132-140 . (2009) MR2664093
  15. Shpakovich, V. P., Muntyan, V. I., Method of averaging for differential equations with maxima, Ukr. Math. J. 39 (1987), 543-545 translation from Ukr. Mat. Zh. 39 1987 662-665 9999DOI99999 10.1007/BF01066476 . (1987) Zbl0716.34090MR0916865
  16. Smirnov, G. V., 10.1090/gsm/041, Graduate Studies in Mathematics 41. AMS, Providence (2002). (2002) Zbl0992.34001MR1867542DOI10.1090/gsm/041

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