Geodesic
Periodic solutions of a class of second order neutral differential equations with multiple different delays
Ural mathematical journal, Tome 8 (2022) no. 2, pp. 71-80 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The present work mainly probes into the existence and uniqueness of periodic solutions for a class of second-order neutral differential equations with multiple delays. Our approach is based on using Banach and Krasnoselskii's fixed point theorems as well as the Green's function method. Besides, two examples are exhibited to validate the effectiveness of our findings which complement and extend some relevant ones in the literature.
Keywords: fixed point theorem, Green's function, neutral differential equation, periodic solutions. 
@article{UMJ_2022_8_2_a5,
     author = {Rabah Khemis and Abdelouaheb Ardjouni and Ahl\'eme Bouakkaz},
     title = {Periodic solutions of a class of second order neutral differential equations with multiple different delays},
     journal = {Ural mathematical journal},
     pages = {71--80},
     year = {2022},
     volume = {8},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/UMJ_2022_8_2_a5/}
}
TY  - JOUR
AU  - Rabah Khemis
AU  - Abdelouaheb Ardjouni
AU  - Ahléme Bouakkaz
TI  - Periodic solutions of a class of second order neutral differential equations with multiple different delays
JO  - Ural mathematical journal
PY  - 2022
SP  - 71
EP  - 80
VL  - 8
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/UMJ_2022_8_2_a5/
LA  - en
ID  - UMJ_2022_8_2_a5
ER  - 
%0 Journal Article
%A Rabah Khemis
%A Abdelouaheb Ardjouni
%A Ahléme Bouakkaz
%T Periodic solutions of a class of second order neutral differential equations with multiple different delays
%J Ural mathematical journal
%D 2022
%P 71-80
%V 8
%N 2
%U http://geodesic.mathdoc.fr/item/UMJ_2022_8_2_a5/
%G en
%F UMJ_2022_8_2_a5
Rabah Khemis; Abdelouaheb Ardjouni; Ahléme Bouakkaz. Periodic solutions of a class of second order neutral differential equations with multiple different delays. Ural mathematical journal, Tome 8 (2022) no. 2, pp. 71-80. http://geodesic.mathdoc.fr/item/UMJ_2022_8_2_a5/

[1] Ardjouni A., Djoudi A., “Existence of positive periodic solutions for a second-order nonlinear neutral differential equation with variable delay”, Adv. Nonlinear Anal., 2:2 (2013), 151–161 | DOI

[2] Ardjouni A., Djoudi A., “Periodic solutions for a second-order nonlinear neutral differential equation with variable delay”, Electron. J. Differ. Equ., 2011:128 (2011), 1–7 URL: https://ejde.math.txstate.edu/Volumes/2011/128/ardjouni.pdf

[3] Bouakkaz A., Ardjouni A., Djoudi A., “Existence of positive periodic solutions for a second-order nonlinear neutral differential equation by the Krasnoselskii's fixed point theorem”, Nonlinear Dyn. Syst. Theory, 17:3 (2017), 230–238 URL: https://e-ndst.kiev.ua/v17n3/2(60).pdf

[4] Bouakkaz A., Ardjouni A., Djoudi A., “Periodic solutions for a second order nonlinear functional differential equation with iterative terms by Schauder's fixed point theorem”, Acta Math. Univ. Comen., 87:2 (2018), 223–235 URL: http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/671/621

[5] Bouakkaz A., Khemis R., “Positive periodic solutions for a class of second-order differential equations with state-dependent delays”, Turkish J. Math., 44:4 (2020), 1412–1426 | DOI

[6] Burton T. A., Stability by Fixed Point Theory for Functional Differential Equations, Dover Publications, New York, 2006, 368 pp.

[7] Guerfi A., Ardjouni A., “Periodic solutions for second order totally nonlinear iterative differential equations”, J. Anal., 30 (2022), 353–367 | DOI

[8] Kaufmann E. R., “A nonlinear neutral periodic differential equation”, Electron. J. Differ. Equ., 2010:88 (2010), 1–8 URL: https://ejde.math.txstate.edu/Volumes/2010/88/kaufmann.pdf

[9] Khemis R., Ardjouni A., Djoudi A., “Existence of periodic solutions for a second-order nonlinear neutral differential equation by the Krasnoselskii's fixed point technique”, Matematiche, 72:1 (2017), 145–156 | DOI

[10] Liu Y., Ge W., “Positive periodic solutions of nonlinear Duffing equations with delay and variable coefficients”, Tamsui Oxf. J. Math. Sci., 20:2 (2004), 235–255

[11] Smart D. S., Fixed Point Theorems., Cambridge Univ. Press, Cambridge, UK, 1980, 104 pp.

[12] Wang Y., Lian H., Ge W., “Periodic solutions for a second order nonlinear functional differential equation”, Appl. Math. Lett., 20:1 (2007), 110–115 | DOI

[13] Yankson E., “Positive periodic solutions for second-order neutral differential equations with functional delay”, Electron. J. Differ. Equ., 2012:14 (2012), 1–6 URL: http://ejde.math.txstate.edu/Volumes/2012/14/yankson.pdf

[14] Zeidler E., Applied Functional Analysis, Springer-Verlag, New York, 1995, 481 pp. | DOI