A NOTE ON THE AVERAGING METHOD FOR DIFFERENTIAL EQUATIONS WITH MAXIMA

Subject Areas : Operation Research

Victor Plotnikov ¹ , Olga Kichmarenko ²

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

Received: 2009-05-07 Accepted : 2009-06-25 Published : 2009-07-01

Keywords:

References:

[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.