# Method of averaging for the system of functional-differential inclusions

Teresa Janiak; Elżbieta Łuczak-Kumorek

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (1996)

- Volume: 16, Issue: 2, page 137-151
- ISSN: 1509-9407

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topTeresa Janiak, and Elżbieta Łuczak-Kumorek. "Method of averaging for the system of functional-differential inclusions." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 16.2 (1996): 137-151. <http://eudml.org/doc/275882>.

@article{TeresaJaniak1996,

abstract = {The basic idea of this paper is to give the existence theorem and the method of averaging for the system of functional-differential inclusions of the form
⎧$ẋ(t) ∈ F(t,x_t,y_t)$ (0)
⎨
⎩$ẋ(t) ∈ G(t,x_t,y_t)$ (1)},

author = {Teresa Janiak, Elżbieta Łuczak-Kumorek},

journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},

keywords = {multifunctions; differential inclusions; functional-differential inclusions; averaging theorems},

language = {eng},

number = {2},

pages = {137-151},

title = {Method of averaging for the system of functional-differential inclusions},

url = {http://eudml.org/doc/275882},

volume = {16},

year = {1996},

}

TY - JOUR

AU - Teresa Janiak

AU - Elżbieta Łuczak-Kumorek

TI - Method of averaging for the system of functional-differential inclusions

JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization

PY - 1996

VL - 16

IS - 2

SP - 137

EP - 151

AB - The basic idea of this paper is to give the existence theorem and the method of averaging for the system of functional-differential inclusions of the form
⎧$ẋ(t) ∈ F(t,x_t,y_t)$ (0)
⎨
⎩$ẋ(t) ∈ G(t,x_t,y_t)$ (1)

LA - eng

KW - multifunctions; differential inclusions; functional-differential inclusions; averaging theorems

UR - http://eudml.org/doc/275882

ER -

## References

top- [1] N.N. Bogolubov, On some statistical methods in mathematical physics, Izv. Acad. Nauk USSR, Lwow 1945.
- [2] M. Dawidowski, On some generalizations of Bogolubov averaging theorem, Funct. et Approx. 7 (1979), 55-70. Zbl0422.34013
- [3] A.F. Filippov, Classical solutions of differential equations with multivalued right-hand side, SIAM, J. Control 5 (1967), 609-621.
- [4] M.M. Hapajev, O.P. Fiatov, O principie usrednijanija dla sistiem s bystrymi i miedljennymi opriemiennymi, Diff. Uravn. 19 (9) (1983), 1640-1643.
- [5] T. Janiak, E. Łuczak-Kumorek, The theorem of middling for functional-differential equations neutral type, Discuss. Math. 11 (1991) 63-73. Zbl0754.34040
- [6] T. Janiak E. Łuczak-Kumorek, A theorem on partial middling for functional-differential equations of the neutral type, Review of research, Faculty of Science, Univ. of Novi Sad, Math. Series 16 (2) (1986). Zbl0651.34065
- [7] T. Janiak, E. uczak-Kumorek, Method of averaging for integral-differential inclusions, Studia Univ. Babes Bolyai, Math. 39 (2) 1994.
- [8] S.S. Klimczuk, Averaging of differential inclusions with unbounded right-hand side, Ukr. Math. Zhurnal 3 (1989), 389-391 (Russian).
- [9] W.A. Plotnikov, The averaging method for differential inclusions and his application in control theory, Diff. Uravn. 15 (8) (1979), 1427-1433 (Russian).
- [10] W.A. Plotnikov, L. Mussa, Obosnowanie adnoj schemy czasticznowo usrednienia dla sistem z midliennymi i bystrymi pieriemiennymi, Diff. Uravn. 28 (4) (1992), 428-432.

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