A note on the averaging method for differential equations with maxima
الموضوعات :
Victor Plotnikov
1
(Department of Optimal Control and Economic Cybernetics Odessa National I.I. Mechnikov University Dvoryanskaya str., 2, Odessa, 65026, Ukraine)
Olga Kichmarenko
2
(Department of Optimal Control and Economic Cybernetics Odessa National I.I. Mechnikov University Dvoryanskaya str., 2, Odessa, 65026, Ukraine)
الکلمات المفتاحية: Averaging method, Differential equations with delay, Differential equations with maxima, Automatic regulation,
ملخص المقالة :
Substantiation of the averaging method for differential equations with maxima is presented. Two theorems on substantiates for differential equations with maxima are established.
[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.
