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'Et moi, ..., si j'avait su comment en revenir, One service mathematics has rendered the human race. It has put common sense back je n'y serais point aile.' where it belongs, on the topmost shelf next Jules Verne to the dusty canister labelled 'discarded n- sense'. The series is divergent; therefore we may be Eric T. Bell able to do something with it. O. Hcaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non- linearities abound. Similarly, all kinds of parts of mathematics seNe as tools for other parts and for other sciences. Applying a...

In contrast to other books devoted to the averaging method and the method of integral manifolds, in the present book we study oscillation systems with many varying frequencies. In the process of evolution, systems of this type can pass from one resonance state into another. This fact considerably complicates the investigation of nonlinear oscillations.

In the present monograph, a new approach based on exact uniform estimates of oscillation integrals is proposed. On the basis of this approach, numerous completely new results on the justification of the averaging method and its...

The book is devoted to the theory of generalized inverses of operators in a Banach space and its applications to linear and weakly nonlinear boundary-value problems for various classes of functional-differential equations, including systems of ordinary differential and difference equations, systems of differential equations with delay, systems with impulse action, and integro-differential systems.

Many problems in celestial mechanics, physics and engineering involve the study of oscillating systems governed by nonlinear ordinary differential equations or partial differential equations. This volume represents an important contribution to the available methods of solution for such systems.
The contents are divided into six chapters. Chapter 1 presents a study of periodic solutions for nonlinear systems of evolution equations including differential equations with lag, systems of neutral type, various classes of nonlinear systems of integro-differential equations, etc. A...