✨
AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
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.
📌 3 Key Takeaways
🎯
Objective & Hypothesis: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.
📊
Key Findings & Data: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.
💡
Conclusion & Impact: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.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Large contraction · Volterra difference equation · infinite delay
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.
🔖
Cite This Article
ELOE, P., JONNALAGADDA, J., RAFFOUL, Y. (2019). The large contraction principle and existence of periodic solutions for infinite delay Volterra difference equations. Turkish Journal of Mathematics, Cilt: 43 - Sayı: 4, 1988–1999. https://ajindex.com/articles/208989