On \(l^ p\) solutions of discrete Volterra equations
type: Item
instance of: scholarly article
title: On \(l^ p\) solutions of discrete Volterra equations
zbMATH Open document ID: 0758.39001
DOI: 10.1007/BF01835701
author: Marian Kwapisz
published in: Aequationes Mathematicae
publication date: 1993-01-16T00:00:00Z
full work available at URL: https://eudml.org/doc/137462
review text: Sufficient conditions are obtained to ensure the solution of \(u(n)=\sum^{n-1}_{i=0}f(n,i,u(i))+g(n)\), a discrete analogue of a nonlinear Volterra integral equation, is in the space \(\ell_ \omega^ p(N,B)\), the space of functions from \(N\) to \(B\) which satisfy \(\sup_{n\geq 0}(\omega^{-1}(n)\sum^{n-1}_{i=0}\| x(i)\|^ p)<\infty\) for some \(\omega:N\to[0,\infty)\) with \(\omega(n)\neq 0\), \(N=\{0,1,2,3,\dots\}\), \((B,\|\cdot\|)\) a Banach space and fixed \(p\), \(1\leq p<\infty\). \((f:N\times N\times B\to B\), \(g:N\to B\), and \(u:N\to B)\). Similar results are obtained for discrete operator equations.
Mathematics Subject Classification ID: 39A10
Mathematics Subject Classification ID: 39A12
Mathematics Subject Classification ID: 47J05
zbMATH DE Number: 92520
zbMATH Keywords: discrete Volterra equation
zbMATH Keywords: \(lp\) solution
zbMATH Keywords: nonlinear difference equation
zbMATH Keywords: Banach space
zbMATH Keywords: discrete operator equations
MaRDI profile type: Publication
cites work: Bielecki's method, existence and uniqueness results for Volterra integral equations in \(L^ p\) space
cites work: Remarks on the existence and uniqueness of solutions of Volterra functional equations in \(L^ p\) spaces
OpenAlex ID: W4248458652
description: scientific article; zbMATH DE number 92520