Study of periodic solutions for third-order iterative differential equations via Krasnoselskii-Burton’s theorem

Abderrahim Guerfi; Abdelouaheb Ardjouni

doi:10.2478/ausm-2022-0005

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Study of periodic solutions for third-order iterative differential equations via Krasnoselskii-Burton’s theorem

Acta Universitatis Sapientiae, Mathematica

Volume 14 (2022): Issue 1 (November 2022)

By: Abderrahim Guerfi and Abdelouaheb Ardjouni

Open Access

|Nov 2022

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Abstract

This paper studies the existence of periodic solutions of a third order iterative differential equation. The main tool used here is Krasnoselskii-Burton’s fixed point theorem dealing with a sum of two mappings, one is a large contraction and the other is compact.

[1] M. Adivar and Y. N. Ra oul, Existence of periodic solutions in totally nonlinear delay dynamic equations, Electron. J. Qual. Theory Differ. Equ., 2009 (1) (2009), 1–20.10.14232/ejqtde.2009.4.1
Open DOI Search in Google Scholar Back to article
[2] P. Andrzej, On some iterative-differential equations III, Zeszyty Naukowe UJ. Prace Mat., 15 (1971), 125–1303.
Search in Google Scholar Back to article
[3] P. Andrzej, On some iterative-differential equations II, Zeszyty Naukowe UJ. Prace Mat., 13 (1969), 49–51.
Search in Google Scholar Back to article
[4] P. Andrzej, On some iterative-differential equation I, Zeszyty Naukowe UJ. Prace Mat., 12 (1968), 53–56.
Search in Google Scholar Back to article
[5] A. Ardjouni and A. Djoudi, Existence of positive periodic solutions for a nonlinear neutral differential equations with variable delay, Appl. Math. E-Notes, 12 (2012), 94–101.
Search in Google Scholar Back to article
[6] C. Babbage, An essay towards the calculus of functions, Philos. Trans. R. Soc. Lond., 105 (1815), 389–432.10.1098/rstl.1815.0024
Open DOI Search in Google Scholar Back to article
[7] A. Bouakkaz, A. Ardjouni and A. Djoudi, Periodic solutions for a nonlinear iterative functional differential equation, Electron. J. Math. Anal. Appl., 7 (1) (2019), 156–166.
Search in Google Scholar Back to article
[8] A. Bouakkaz, A. Ardjouni and A. Djoudi, Periodic solutions for a second order nonlinear functional differential equation with iterative terms by Schauder fixed point theorem, Acta Math. Univ. Comen., LXXXVII (2) (2018), 223–235.10.1007/s40590-019-00267-x
Open DOI Search in Google Scholar Back to article
[9] A. Bouakkaz, A. Ardjouni, R. Khemis and A. Djoudi, Periodic solutions of a class of third-order functional differential equations with iterative source terms, Bol. Soc. Mat. Mex., 26 (2020), 443–458.10.1007/s40590-019-00267-x
Open DOI Search in Google Scholar Back to article
[10] T. A. Burton, Stability by Fixed Point Theory for Functional Differential Equations, Dover Publications, New York, 2006.
Search in Google Scholar Back to article
[11] Z. Cheng and J. Ren, Existence of positive periodic solution for variable-coe cient third order differential equation with singularity, Math. Methods Appl. Sci., 37 (2014), 2281–2289.10.1002/mma.2975
Open DOI Search in Google Scholar Back to article
[12] Y. Chen, J. Ren and S. Siegmund, Green’s function for third-order differential equations, Rocky Mt. J. Math. 41 (5) (2011), 1417–1448.10.1216/RMJ-2011-41-5-1417
Open DOI Search in Google Scholar Back to article
[13] Y. Liu and W. Ge, Positive periodic solutions of nonlinear Du ng equations with delay and variable coe cients, Tamsui Oxf. J. Math. Sci., 20 (2004), 235–255.
Search in Google Scholar Back to article
[14] F. Nouioua, A. Ardjouni and A. Djoudi, Periodic solutions for a third-order delay differential equation, Appl. Math. E-Notes, 16 (2016), 210–221.
Search in Google Scholar Back to article
[15] F. Nouioua, A. Ardjouni, A. Merzougui and A. Djoudi, Existence of positive periodic solutions for a third-order delay differential equation, Int. J. Anal. Appl., 13 (2) (2017), 136–143.
Search in Google Scholar Back to article
[16] J. Ren, S. Siegmund and Y. Chen, Positive periodic solutions for third-order nonlinear differential equations, Electron. J. Differ. Equ., 2011 (66) (2011), 1–19.10.14232/ejqtde.2011.1.65
Open DOI Search in Google Scholar Back to article
[17] Y. Wang, H. Lian and W. Ge, Periodic solutions for a second order nonlinear functional differential equation, Appl. Math. Lett., 20 (2007), 110–115.10.1016/j.aml.2006.02.028
Open DOI Search in Google Scholar Back to article
[18] P. Zhang, Analytic solutions for iterative functional-differential equations, Electron. J. Differ. Equ., 2012 (180) (2012), 1–7.10.14232/ejqtde.2012.1.25
Open DOI Search in Google Scholar Back to article
[19] H. Y. Zhao and M. Feckan, Periodic solutions for a class of differential equations with delays depending on state, Math. Commun., 22 (2017), 1–14.
Search in Google Scholar Back to article
[20] H. Y. Zhao and J. Liu, Periodic solutions of an iterative functional differential equation with variable coe cients, Math. Methods Appl. Sci., 40 (2017), 286–292.10.1002/mma.3991
Open DOI Search in Google Scholar Back to article

Articles in this issue

DOI: https://doi.org/10.2478/ausm-2022-0005 | Journal eISSN: 2066-7752

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Language: English

Page range: 75 - 89

Submitted on: Mar 19, 2021

Published online: Nov 18, 2022

Published in print: Nov 1, 2022

Published by: Sapientia Hungarian University of Transylvania

In partnership with: Paradigm Publishing Services

Keywords:

Krasnoselskii-Burton’s fixed point,

large contraction,

iterative differential equations,

periodic solution,

Green’s function

MSC:

34K13,

34A34,

34K30,

34L30

Related subjects:

Mathematics,

General mathematics

© 2022 Abderrahim Guerfi, Abdelouaheb Ardjouni, published by Sapientia Hungarian University of Transylvania
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 14 (2022): Issue 1 (November 2022)