Document Type : Technical Note

Authors

Department of Optimal Control and Economic Cybernetics Odessa National I.I. Mechnikov University Dvoryanskaya str., 2, Odessa, 65026, Ukraine

Abstract

Substantiation of the averaging method for differential equations with maxima is presented. Two theorems on substantiates for differential equations with maxima are established.

Keywords

[1] Angelov V.G., Bainov D.D., On the functional differential equations with "maximums", Appl. Anal., 16, 187-194, 1983.
[2] Bainov D.D., Milusheva S.D., Justification of the averaging method for functional differential equations with maximums, Hardonic J., 6,1034-1039, 1983.
[3] Bainov D.D., Voulov H.D., Differential Equation with Maxima. Stability of Solutions, Sofia, 1992.
[4] Bainov D.D., Zahariev A.I., Oscillating and asymptotic properties of a class of functional differential equations with maxima, Czechoslovak Math. J., 34 (109), 247-251, 1984.
[5] Magomedov A.R., Some questions of differential-equations with maximums, Izv. Akad. Nauk Azerb. SSR, Ser. Fiz.-Tek. i Mat. Nauk, 1, 104-108, 1977.
[6] Milusheva S., Bainov D.D., Justification of the averaging method for multipoint boundary value problems for a class of functional differential equations with maximums. Collect. Math., 37, 297-304, 1986.
[7] Mishev D.P., Oscillatory properties of the solutions of hyperbolic differential equations with "maximums", Hiroshima Math. J., 16, 77-83, 1986.
[8] Plotnikov V.A. The averaging method in control problems, Lybid, Kiev-Odessa, 1992.
[9] Plotnokov V.A., Kichmarenko O.D., Averaging of differential equations with maxima, Vestnik Chernovitskogo universiteta, 150, 78-82, 2002.
[10] Popov E.P., Automatic Regulation and Control, Nauka, Moscow, 1966.
[11] Sendov B., Popov V., The averaged smoothness moduli, Mir, Moscow, 1988.