Advances in Difference Equations 
Volume 2004 (2004), Issue 3, Pages 237-248
doi:10.1155/S1687183904310101

A functional-analytic method for the study of difference equations

Eugenia N. Petropoulou1 and Panayiotis D. Siafarikas2

 1Department of Engineering Sciences, Division of Applied Mathematics and Mechanics, University of Patras, Patras 26500, Greece
2Department of Mathematics, University of Patras, Patras 26500, Greece
Received 29 October 2003; Revised 10 February 2004

Abstract

We will give the generalization of a recently developed functional-analytic method for studying linear and nonlinear, ordinary and partial, difference equations in the ℓp1 and ℓp2 spaces, p∈ℕ, p≥1. The method will be illustrated by use of two examples concerning a nonlinear ordinary difference equation known as the Putnam equation, and a linear partial difference equation of three variables describing the discrete Newton law of cooling in three dimensions.