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Book review

Author(s) Sharkovsky, A.N.
Maistrenko, Yu.L.
Romanenko, L.Yu.
Title Difference equations and their applications
Publisher Kluwer Academic Publishers
Year of publication 1993
Reviewed by Gh. Toader

Difference equations reflect one of the essential properties of the real world - its discreteness. The declared aim of this book is the presentation of some unusual properties of solutions of nonlinear difference equations. These properties make the difference equations useful in order to model some processes (especially in those cases when it is difficult to apply ordinary differential equations).

The book is divided in four parts. The first part is devoted to the theory of one-dimensional dynamical systems. In the second part are described the asymptotic properties of the solutions of difference equations with continuous argument. The third part is devoted to differential-difference equations which are close to difference ones. In the fourth part it is developed a method of investigation of nonlinear boundary-value problem for hyperbolic systems which is based on the reduction of these to differential-difference equations.

The first author is well known as a researcher in difference equations. In fact all the authors are experts in this field and many results presented here are published for the first time.

The monograph will be useful for specialists in difference and differential equations as well as in applied mathematics (physics, chemistry, biology).