Discrete Oscillation Theory

This book is devoted to a rapidly developing branch of thequalitative theory of difference equations with or without delays.It presents the theory of oscillation of difference equations, exhibiting classical as well as very recent results in that area.While there are several books on difference equations and also onoscillation theory for ordinary differential equations, there isuntil now no book devoted solely to oscillation theory fordifference equations. This book is filling the gap, and it caneasily be used as an encyclopedia and reference tool for discreteoscillation theory. In nine chapters, the book covers a wide rangeof subjects, including oscillation theory for second-order lineardifference equations, systems of difference equations, half-lineardifference equations, nonlinear difference equations, neutraldifference equations, delay difference equations, and differentialequations with piecewise constant arguments. This book summarizesalmost 300 recent research papers and hence covers all aspects ofdiscrete oscillation theory that have been discussed in recentjournal articles. The presented theory is illustrated with 121examples throughout the book. Each chapter concludes with asection that is devoted to notes and bibliographical andhistorical remarks. The book is addressed to a wide audience ofspecialists such as mathematicians, engineers, biologists, andphysicists. Besides serving as a reference tool for researchers indifference equations, this book can also be easily used as atextbook for undergraduate or graduate classes. It is written at alevel easy to understand for college students who have had coursesin calculus