Smoothness of solutions for delay-difference equations
type: Item
instance of: scholarly article
title: Smoothness of solutions for delay-difference equations
zbMATH Open document ID: 0809.39004
DOI: 10.1016/0898-1221(94)00100-6
author: Johnny Henderson
publication date: 1994-09-21T00:00:00Z
review text: A real difference equation of the form (1) \(x(n+1) = f(n,x(n), x(n-k_ n))\), \(n \geq 0\), is considered. Here \(k_ n \in \{0, \dots, r\}\) for all \(n \geq 0\) and for some nonnegative integer \(r\). It is assumed that the partial derivatives of \(f\) with respect to the second and third variable are continuous. For \((a_ 0, \dots, a_ r) \in \mathbb{R}^{r+1}\) let \(x(n, a_ 0, \dots, a_ r)\) denote the solution of (1) satisfying the initial condition \((x(-r), \dots, x(0)) = (a_ 0, \dots, a_ r)\). It is proved that the partial derivatives of \(x\) with respect to its last \(r+1\) variables exist.
reviewed by: Helmut Länger
Mathematics Subject Classification ID: 39A10
zbMATH DE Number: 641438
zbMATH Keywords: smoothness of solutions
zbMATH Keywords: delay-difference equations
zbMATH Keywords: partially differentiable solution
MaRDI profile type: Publication
full work available at URL: 0898-1221(94)00100-6
OpenAlex ID: W2036234203
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published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 641438