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Journals / Turkish Journal of Mathematics / 2019 / Cilt: 43 - Sayı: 4

The large contraction principle and existence of periodic solutions for infinite delay Volterra difference equations

Youssef RAFFOUL
Paul ELOE
Jagan Mohan JONNALAGADDA
Pages
1988–1999
Publication Date
2022-11-05
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

The primary sufficient condition isnot verifiable in terms of the parameters of the difference equation, and so we provide three applications in which theprimary sufficient condition is verified.

📌 3 Key Takeaways

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Objective & Hypothesis:In this article, we establish sufficient conditions for the existence of periodic solutions of a nonlinear infinitedelay Volterra difference equation: mathrm{Δx}(n)=p(n)+b(n)h(x(n))+sum_{mathrm k=-infty}^{mathrm n}B(n,k)g(x(k)).We employ a Krasnosel’skiĭ type fixed point theorem, originally proved by Burton.
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Key Findings & Data:In this article, we establish sufficient conditions for the existence of periodic solutions of a nonlinear infinitedelay Volterra difference equation: mathrm{Δx}(n)=p(n)+b(n)h(x(n))+sum_{mathrm k=-infty}^{mathrm n}B(n,k)g(x(k)).We employ a Krasnosel’skiĭ type fixed point theorem, originally proved by Burton.
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Conclusion & Impact:The primary sufficient condition isnot verifiable in terms of the parameters of the difference equation, and so we provide three applications in which theprimary sufficient condition is verified.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

In this article, we establish sufficient conditions for the existence of periodic solutions of a nonlinear infinitedelay Volterra difference equation: mathrm{Δx}(n)=p(n)+b(n)h(x(n))+sum_{mathrm k=-infty}^{mathrm n}B(n,k)g(x(k)).We employ a Krasnosel’skiĭ type fixed point theorem, originally proved by Burton. The primary sufficient condition isnot verifiable in terms of the parameters of the difference equation, and so we provide three applications in which theprimary sufficient condition is verified.

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Cite This Article

RAFFOUL, Y., ELOE, P., JONNALAGADDA, J. M. (2022). 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/607967

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References (6)

  1. Adivar M, Islam M, Raffoul YN. Separate contraction and existence of periodic solutions in totally nonlinear delay differential equations. Hacettepe Journal of Mathematics and Statistics 2012; 41 (1): 1-13
  2. Avramescu C. Some remarks on Krasnosel’skiĭ’s fixed point theorem. Electronic Journal of Qualitative Theory of Differential Equations 2003; (4): 1-15. doi: 10.14232/ejqtde.2003.1.5 [3] Bota M, Ilea V, Petruşel A. Krasnosel’skiĭ’s theorem in generalized b-Banach spaces and applications. Journal of Nonlinear Convex Analysis 2017; 18 (4): 575-587
  3. Burton TA. Stability and Periodic Solutions of Ordinary and Functional Differential Equations. New York, NY, USA: Elsevier, 1985
  4. Burton TA. Integral equations, implicit functions and fixed points. Proceedings of the American Mathematical Society 1996; 124 (8): 2383-2390. doi: 10.1090/S0002-9939-96-03533-2 [6] Burton TA. Liapunov functionals, fixed points, and stability by Krasnosel’skiĭ’s theorem. Nonlinear Studies 2002; 9 (2): 181-190
  5. Burton TA, Purnaras IK. A unification theory of Krasnosel’skiĭ for differential equations. Nonlinear Analysis 2013; 89: 121-133. doi: 10.1016/j.na.2013.05.007 [8] Burton TA, Zhang B. Fractional equations and generalizations of Schaefer’s and Krasnosel’sliĭ’s fixed point theorems. Nonlinear Analysis 2012; 75 (18): 6485-6495. doi: 10.1016/j.na.2012.07.022 [9] Derrardjia I, Ardjouni A, Djoudi A. Stability by Krasnosel’skiĭ’s theorem in totally nonlinear neutral differential equations. Opuscula Mathematica 2013; 33 (2): 255-272. doi: 10.7494/OpMath.2013.33.2.255 [10] Essel E, Yankson E. On the existence of positive periodic solutions for totally nonlinear neutral differential equations of the second-order with functional delay. Opuscula Mathematica 2014; 34 (3): 469-481. doi: 10.7494/Op- Math.2014.34.3.469 [11] Krasnosel’skiĭ MA. Some Problems of Nonlinear Analysis. American Mathematical Society Translations, Series 2. Providence, RI, USA: AMS, 1958
  6. Mesmouli MB, Ardjouni A, Djoudi A. Study of the periodic or nonnegative periodic solutions of functional differential equations via Krasnosel’skiĭ-Burton’s theorem. Differential Equations and Dynamical Systems 2016; 24 (4): 391-406. doi: 10.1007/s12591-014-0235-5 [13] Park S. Generalizations of the Krasnosel’skiĭ fixed point theorem. Nonlinear Analysis 2007; 67 (12): 3401-3410. doi: 10.1016/j.na.2006.10.024 [14] Petre I, Petruşel A. Krasnosel’skiĭ’s theorem in generalized Banach spaces and applications. Electroni