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By Professor Yu. A. Mitropolskii, Professor Nguyen Van Dao (auth.)

Many dynamical platforms are defined via differential equations that may be separated into one half, containing linear phrases with consistent coefficients, and a moment half, quite small in comparison with the 1st, containing nonlinear phrases. one of these approach is related to be weakly nonlinear. The small phrases rendering the method nonlinear are often called perturbations. A weakly nonlinear method is named quasi-linear and is ruled by means of quasi-linear differential equations. we'll have an interest in platforms that lessen to harmonic oscillators within the absence of perturbations. This publication is dedicated essentially to utilized asymptotic tools in nonlinear oscillations that are linked to the names of N. M. Krylov, N. N. Bogoli­ ubov and Yu. A. Mitropolskii. some great benefits of the current equipment are their simplicity, particularly for computing larger approximations, and their applicability to a wide classification of quasi-linear difficulties. during this booklet, we confine ourselves basi­ cally to the scheme proposed through Krylov, Bogoliubov as said within the monographs [6,211. We use those equipment, and in addition enhance and enhance them for fixing new difficulties and new sessions of nonlinear differential equations. even supposing those equipment have many functions in Mechanics, Physics and approach, we are going to illustrate them in basic terms with examples which truly convey their energy and that are themselves of serious curiosity. a certain quantity of extra complicated fabric has additionally been integrated, making the ebook appropriate for a senior non-obligatory or a starting graduate direction on nonlinear oscillations.

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