Next Article in Journal
An Overview of Generalized Gamma Mittag–Leffler Model and Its Applications
Next Article in Special Issue
On Limiting Behavior of Contaminant Transport Models in Coupled Surface and Groundwater Flows
Previous Article in Journal
On the Fractional Poisson Process and the Discretized Stable Subordinator
Article Menu

Export Article

Open AccessArticle
Axioms 2015, 4(3), 345-364; doi:10.3390/axioms4030345

Almost Periodic Solutions of Nonlinear Volterra Difference Equations with Unbounded Delay

1
Department of Information Science, Okayama University of Science, 1-1 Ridai-cho, Okayama 700-0005, Japan
2
Department of Industrial Information, Iwate Prefectural University, Miyako College, 1-5-1 Kanan,Miyako, Iwate 027-0039, Japan
*
Author to whom correspondence should be addressed.
Academic Editor: Constantin Corduneanu
Received: 27 June 2015 / Revised: 11 August 2015 / Accepted: 18 August 2015 / Published: 24 August 2015
(This article belongs to the Special Issue Functional Differential Equations)
View Full-Text   |   Download PDF [274 KB, uploaded 24 August 2015]

Abstract

In order to obtain the conditions for the existence of periodic and almost periodic solutions of Volterra difference equations, \( x(n+1)=f(n,x(n))+\sum_{s=-\infty}^{n}F(n,s, {x(n+s)},x(n)) \), we consider certain stability properties, which are referred to as (K, \( \rho \))-weakly uniformly-asymptotic stability and (K, \( \rho \))-uniformly asymptotic stability. Moreover, we discuss the relationship between the \( \rho \)-separation condition and the uniformly-asymptotic stability property in the \( \rho \) sense. View Full-Text
Keywords: almost periodic solutions; Volterra difference equations; (K, p)-relatively weakly uniformly-asymptotically stable; p-separation conditions almost periodic solutions; Volterra difference equations; (K, p)-relatively weakly uniformly-asymptotically stable; p-separation conditions
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

Scifeed alert for new publications

Never miss any articles matching your research from any publisher
  • Get alerts for new papers matching your research
  • Find out the new papers from selected authors
  • Updated daily for 49'000+ journals and 6000+ publishers
  • Define your Scifeed now

SciFeed Share & Cite This Article

MDPI and ACS Style

Hamaya, Y.; Itokazu, T.; Saito, K. Almost Periodic Solutions of Nonlinear Volterra Difference Equations with Unbounded Delay. Axioms 2015, 4, 345-364.

Show more citation formats Show less citations formats

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Axioms EISSN 2075-1680 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top