Turkish Journal of Mathematics
DOI
10.3906/mat-1904-128
Abstract
In this article, we establish sufficient conditions for the existence of periodic solutions of a nonlinear infinite delay Volterra difference equation: $$\Delta x(n) = p(n) + b(n)h(x(n)) + \sum^{n}_{k = -\infty}B(n, k)g(x(k)).$$ We employ a Krasnosel'ski\u{i} type fixed point theorem, originally proved by Burton. The primary sufficient condition is not verifiable in terms of the parameters of the difference equation, and so we provide three applications in which the primary sufficient condition is verified.
Keywords
Large contraction, Volterra difference equation, infinite delay, periodic solution, fixed point
First Page
1988
Last Page
1999
Recommended Citation
Eloe, Paul; JONNALAGADDA, JAGANMOHAN; and RAFFOUL, YOUSSEF
(2019)
"The large contraction principle and existence of periodic solutions for infinite delay Volterra difference equations,"
Turkish Journal of Mathematics: Vol. 43:
No.
4, Article 14.
https://doi.org/10.3906/mat-1904-128
Available at:
https://journals.tubitak.gov.tr/math/vol43/iss4/14
