Existence and Boundedness of Solutions for Nonlinear Volterra Difference Equations in Banach Spaces

Author:

Medina Rigoberto1ORCID

Affiliation:

1. Departamento de Ciencias Exactas, Universidad de Los Lagos, Casilla 933, Osorno, Chile

Abstract

We consider a class of nonlinear discrete-time Volterra equations in Banach spaces. Estimates for the norm of operator-valued functions and the resolvents of quasi-nilpotent operators are used to find sufficient conditions that all solutions of such equations are elements of an appropriate Banach space. These estimates give us explicit boundedness conditions. The boundedness of solutions to Volterra equations with infinite delay is also investigated.

Funder

Dirección de Investigación

Publisher

Hindawi Limited

Subject

Applied Mathematics,Analysis

Cited by 2 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Asymptotic behavior of solutions to difference equations in Banach spaces;Electronic Journal of Qualitative Theory of Differential Equations;2021

2. Stability for Linear Volterra Difference Equations in Banach Spaces;Abstract and Applied Analysis;2018

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