Method of averaging for the system of functional-differential inclusions

• Autorzy: Teresa Janiak , Elżbieta Łuczak-Kumorek
• Języki publikacji: EN

Abstrakty

EN

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)

Słowa kluczowe

EN

multifunctions; differential inclusions

Kategorie tematyczne

• 34C29: Averaging method
• 34A60: Differential inclusions

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae, Differential Inclusions, Control and Optimization
• Rocznik: 1996
• Tom: 16
• Numer: 2
• Strony: 137-151

Daty

wydano

1996

Twórcy

autor

Teresa Janiak

• Technical University, Institute of Mathematics, Podgórna 50, 65-246 Zielona Góra, Poland

autor

Elżbieta Łuczak-Kumorek

• Technical University, Institute of Mathematics, Podgórna 50, 65-246 Zielona Góra, Poland

Bibliografia

• [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.
• [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.
• [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).
• [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.