Báo Cáo Báo cáo hóa học A FUNCTIONAL-ANALYTIC METHOD FOR THE STUDY OF DIFFERENCE EQUATIONS EUGENIA

A FUNCTIONAL-ANALYTIC METHOD FOR THE STUDY OF DIFFERENCE EQUATIONS EUGENIA N. PETROPOULOU AND PANAYIOTIS D. SIAFARIKAS

Received 29 October 2003 and in revised form 10 February 2004

We will give the generalization of a recently developed functional-analytic method for studying linear and nonlinear, ordinary and partial, difference equations in the 1 and 2 p p 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.


1. Introduction The aim of this paper is to present the generalization of a functional-analytic method, which was recently developed for the study of linear and nonlinear difference equations of one, two, three, and four variables in the Hilbert space