A large amount of work has been done on ordinary differ ential equations with small parameters multiplying deriv atives. This book investigates questions related to the asymptotic calculation of relaxation oscillations, which are periodic solutions formed of sections of both sl- and fast-motion parts of phase trajectories. A detailed discussion of solutions of differential equations involving small parameters is given for regions near singular points. The main results examined were obtained by L. S. Pontryagin and the authors. Other works have also been taken into account: A. A. Dorodnitsyn's investigations of Van der Pol's equation, results obtained by N. A. Zheleztsov and L. V. Rodygin concerning relaxation oscillations in electronic devices, and results due to A. N. Tikhonov and A. B. Vasil'eva concerning differential equations with small parameters multiplying certain derivatives. E. F. Mishchenko N. Kh. Rozov v CONTENTS Chapter I. Dependence of Solutions on Small Parameters. Applications of Relaxation Oscillations 1. Smooth Dependence. Poincare's Theorem . 1 2. Dependence of Solutions on a Parameter, on an Infinite Time Interval 3 3. Equations with Small Parameters 4 Multiplying Derivatives 4. Second-Order Systems. Fast and Slow Motion.

Differential Equations with Small Parameters and Relaxation Oscillations (Mathematical Concepts and Methods in Science and Engineering)

Science & Math

Mishchenko, E. F.

Rozov, B. K.

Goodspeed, F. M. (translator)

Mathematics

Perseus Publishing

<p>Text: English, Russian (translation)</p>

Mathematical Physics and Complex Analysis: A Collection of Survey Papers on the 50th Anniversary of the Institute (Proceedings of the Steklov Institute of Mathematics) (English and Russian Edition)

Bitsadze, A V

Faddeev, L.D.

Gonchar, A. A.

Amer Mathematical Society

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