Geodesic
On the averaging of differential inclusions with maxima
Mathematica Bohemica, Tome 148 (2023) no. 1, pp. 1-10
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

We apply the averaging method to ordinary differential inclusions with maxima perturbed by a small parameter and illustrate the method by some examples.
We apply the averaging method to ordinary differential inclusions with maxima perturbed by a small parameter and illustrate the method by some examples.
DOI : 10.21136/MB.2022.0077-20
Classification : 34A60, 34C29
Keywords: differential inclusion; maxima; averaging 
@article{10_21136_MB_2022_0077_20,
     author = {Bar, Bachir},
     title = {On the averaging of differential inclusions with maxima},
     journal = {Mathematica Bohemica},
     pages = {1--10},
     year = {2023},
     volume = {148},
     number = {1},
     doi = {10.21136/MB.2022.0077-20},
     mrnumber = {4536306},
     zbl = {07655809},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/MB.2022.0077-20/}
}
TY  - JOUR
AU  - Bar, Bachir
TI  - On the averaging of differential inclusions with maxima
JO  - Mathematica Bohemica
PY  - 2023
SP  - 1
EP  - 10
VL  - 148
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.21136/MB.2022.0077-20/
DO  - 10.21136/MB.2022.0077-20
LA  - en
ID  - 10_21136_MB_2022_0077_20
ER  - 
%0 Journal Article
%A Bar, Bachir
%T On the averaging of differential inclusions with maxima
%J Mathematica Bohemica
%D 2023
%P 1-10
%V 148
%N 1
%U http://geodesic.mathdoc.fr/articles/10.21136/MB.2022.0077-20/
%R 10.21136/MB.2022.0077-20
%G en
%F 10_21136_MB_2022_0077_20
Bar, Bachir. On the averaging of differential inclusions with maxima. Mathematica Bohemica, Tome 148 (2023) no. 1, pp. 1-10. doi: 10.21136/MB.2022.0077-20

[1] Aubin, J.-P., Cellina, A.: Differential Inclusions: Set-Valued Maps and Viability Theory. Grundlehren der Mathematischen Wissenschaften 264. Springer, Berlin (1984),\99999DOI99999 10.1007/978-3-642-69512-4 . | MR | JFM

[2] Aubin, J.-P., Frankowska, H.: Set-Valued Analysis. Systems and Control: Foundations and Applications 2. Birkhäuser, Boston (1990),\99999DOI99999 10.1007/978-0-8176-4848-0 . | MR | JFM

[3] Aumann, R. J.: Integrals of set-valued functions. J. Math. Anal. Appl. 12 (1965), 1-12. | DOI | MR | JFM

[4] Bainov, D. D., Hristova, S. G.: Differential Equations with Maxima. Pure and Applied Mathematics (Boca Raton) 298. CRC Press, Boca Raton (2011),\99999DOI99999 10.1201/b10877 . | JFM

[5] Bar, B., Lakrib, M.: Averaging method for ordinary differential inclusions with maxima. Electron. J. Differ. Equ. 2018 (2018), Article ID 115, 12 pages \99999MR99999 3831861 . | MR | JFM

[6] Bourada, A., Guen, R., Lakrib, M., Yadi, K.: Some averaging results for ordinary differential inclusions. Discuss. Math., Differ. Incl. Control Optim. 35 (2015), 47-63. | DOI | MR

[7] Deimling, K.: Multivalued Differential Equations. De Gruyter Series in Nonlinear Analysis and Applications 1. Walter de Gruyter, Berlin (1992),\99999DOI99999 10.1515/9783110874228 . | MR | JFM

[8] Gama, R., Smirnov, G.: Stability and optimality of solutions to differential inclusions via averaging method. Set-Valued Var. Anal. 22 (2014), 349-374. | DOI | MR | JFM

[9] Kichmarenko, O. D.: Averaging of differential equations with Hukuhara derivative with maxima. Int. J. Pure Appl. Math. 57 (2009), 447-457. | MR | JFM

[10] Kichmarenko, O. D., Sapozhnikova, K. Y.: Full averaging scheme for differential equation with maximum. Contemp. Anal. Appl. Math. 3 (2015), 113-122. | DOI | MR | JFM

[11] Klymchuk, S., Plotnikov, A., Skripnik, N.: Overview of V. A. Plotnikov's research on averaging of differential inclusions. Phys. D 241 (2012), 1932-1947. | DOI | MR

[12] Lakrib, M.: An averaging theorem for ordinary differential inclusions. Bull. Belg. Math. Soc. - Simon. Stevin 16 (2009), 13-29. | DOI | MR | JFM

[13] Plotnikov, V. A., Kichmarenko, O. D.: Averaging of differential equations with maxima. Nauk. Visn. Chernivets'kogo Univ., Mat. 150 (2002), 78-82 Ukrainian \99999ZBL99999 1071.34519 .

[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 . | MR

[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 \99999DOI99999 10.1007/BF01066476 . | MR | JFM

[16] Smirnov, G. V.: Introduction to the Theory of Differential Inclusions. Graduate Studies in Mathematics 41. AMS, Providence (2002). | DOI | MR | JFM

Cité par Sources :