Difference equations and inequalities: theory, methods, and applications. 2nd, revised and expanded ed. (English) Zbl 0952.39001

Agarwal, Ravi P.

Pure and Applied Mathematics, Marcel Dekker. 228. New York, NY: Marcel Dekker. xiii, 971 p. (2000).

Dynamical systems in which the time independent variables have only a discrete set of values often lead to mathematical models of discrete event dynamical systems also called finite difference equations. In the past few decades the study of difference equations has already drawn a great deal of attention, not only among mathematicians but from various other disciplines as well. This comes about in large part, from the use of these equations in the formulation and analysis of discrete time systems, numerical integration of differential equations by finite difference schemes and several other fields.
The present book contains a detailed account of the basic theory of finite difference equations and inequalities which find important applications in various mathematical models such as probability theory, stochastic time series, combinatorial analysis, number theory, geometry, electrical networks, genetics in biology, economics, psychology, sociology, etc. It contains thirteen chapters besides extensive lists of references at the end of each chapter.
The book discusses qualitative properties of the solutions of linear and nonlinear difference equations, discrete versions of Rolle’s theorem, the mean value theorem, Taylor’s formula, l’Hospital rule, Kneser’s theorem etc. and investigates the stability and oscillatory properties of solutions of difference equations and explores the study of various types of boundary value problems for difference equations. It also contains fundamental finite difference inequalities and their applications.
The topics are tastefully selected. It is well written and provides an account of the recent developments and is self-contained. It is a nice addition to the literature.

Reviewer: B.G.Pachpatte (Aurangabad)

MSC:

39A10	Additive difference equations
39-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to difference and functional equations
26D15	Inequalities for sums, series and integrals
93C65	Discrete event control/observation systems

Keywords:

discrete event dynamical systems; finite difference equations; discrete time systems; nonlinear difference equations; Rolle’s theorem; mean value theorem; Taylor’s formula; l’Hospital rule; Kneser’s theorem; stability; oscillation; boundary value problems; finite difference inequalities

Citations:

Zbl 0925.39001