This special issue is in recognition of the achievements of Professor Gerasimos Ladas (or ‘Gerry’ as he is fondly called). His vision of making the area of difference equations a distinct and autonomous branch of mathematics has come to fruition after over two decades of hard work and diligence.
His efforts began with a seminar held at the University of Rhode Island. Initially conducted as a seminar on both differential and difference equations, in the early 1990's, it rapidly transformed into a seminar devoted solely to difference equations. The aim of this seminar was to popularize difference equations by bringing together graduate students as well as departmental and visiting faculty and exposing them to a reasonable variety of topics in difference equations. The inspiration for topics started out as coming from an assortment of papers in journals not solely related to theory, but rather to topics in areas such as biology, medicine, economics and the social sciences, as well as to other branches of mathematics. The papers that were chosen from these journals were those that were amenable to re-evaluation in the language of difference equations. Eventually, however, topics derived from outside journals rapidly gave birth to completely unrelated topics pertinent only to difference equations.
This burgeoning growth of topics was an outcome of the many open discussions in the seminar, solicited and mediated by Gerry Ladas and his ‘partner in crime’ Edward Grove, also of the University of Rhode Island. Novel ideas generated by these discussions were ultimately converted into research projects. As Ed Grove once commented, there are ‘gold nuggets in the streets’ yet to be discovered. The research projects were turned into books and papers that were co-authored by graduate students, faculty from within the department and faculty from outside. Finally, the need for a suitable home inspired the co-founding, with Saber Elaydi, of the Journal of Difference Equations and Applications (the JDEA).
Gerry Ladas soon became an internationally renowned figure who regularly gave talks in venues all over the world. Together with Saber Elaydi and many others who volunteered their time and services, he organized the International Society of Difference Equations and the important annual meetings known as International Conference on Difference Equations and Applications. In these and many other venues in the USA and abroad, he gave plenary talks and invited presentations in which he extolled the virtues of difference equations and introduced problems that were usually deceptively simple to describe but whose analysis often lead to significant new inspirations and results.
The latter aspect of Gerry Ladas' work stands out in particular as vintage Ladas and is best illustrated by his famous ‘Open Problems and Conjectures’ presented at conferences and published in the JDEA. Monetary awards were often promised for the more difficult to almost impossible problems which involved otherwise benign-looking equations. In particular, Ladas and colleagues' results on a class of rational difference equations and systems led to substantial progress in the field as well as the formulation of many challenging and important problems.
To this day, many of these problems still present challenges not only to those new to the area of difference equations, but also to well-seasoned researchers in the area of difference equations.
The by-products of success in reaching solutions to these problems are often worth more than the actual solutions themselves. As more and more problems are solved, new tools and theory along the way are discovered that accrue and help to build a solid foundation for the field of difference equations, strengthening the field more and more.
By discovering substantial and deep results as well as selflessly sharing his ideas with students and collaborators and promoting their ideas and carriers, Gerry Ladas contributed enormously to the development and familiarization of the field of difference equations. Thanks to him there are still plenty of gold nuggets in the streets waiting for those new to the field of difference equations and those already experienced within it.