| Title:
|
Analysis of periodic solutions for nonlinear coupled integro-differential systems with variable delays (English) |
| Author:
|
Mansouri, Bouzid |
| Author:
|
Ardjouni, Abdelouaheb |
| Author:
|
Djoudi, Ahcene |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
63 |
| Issue:
|
1 |
| Year:
|
2022 |
| Pages:
|
51-68 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The objective of this work is the application of Krasnosel'skii's fixed point technique to prove the existence of periodic solutions of a system of coupled nonlinear integro-differential equations with variable delays. An example is given to illustrate this work. (English) |
| Keyword:
|
integro-differential equation |
| Keyword:
|
periodic solution |
| Keyword:
|
Krasnosel'skii's fixed point theorem |
| MSC:
|
34K20 |
| MSC:
|
45D05 |
| MSC:
|
45J05 |
| idZBL:
|
Zbl 07584113 |
| idMR:
|
MR4445737 |
| DOI:
|
10.14712/1213-7243.2022.007 |
| . |
| Date available:
|
2022-07-18T11:50:43Z |
| Last updated:
|
2024-04-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/150431 |
| . |
| Reference:
|
[1] Adivar M., Raffoul Y. N.: Existence of periodic solutions in totally nonlinear delay dynamic equations.Electron. J. Qual. Theory Differ. Equ. 2009 (2009), Special Edition I, no. 1., 20 pages. MR 2558826 |
| Reference:
|
[2] Ardjouni A., Djoudi A.: Periodic solutions for a second-order nonlinear neutral differential equation with variable delay.Electron. J. Differential Equations 2011 (2011), no. 128, 7 pages. Zbl 1278.34077, MR 2853014 |
| Reference:
|
[3] Ardjouni A., Djoudi A.: Existence of periodic solutions for a second order nonlinear neutral differential equation with functional delay.Electron. J. Qual. Theory Differ. Equ. 2012 (2012), no. 31, 9 pages. MR 2904111 |
| Reference:
|
[4] Ardjouni A., Djoudi A.: Existence of periodic solutions for a second order nonlinear neutral differential equation with variable delay.Palest J. Math. 3 (2014), no. 2, 191–197. MR 3230706 |
| Reference:
|
[5] Ardjouni A., Djoudi A.: Periodic solutions for a second order nonlinear neutral functional differential equation with variable delay.Matematiche (Catania) 69 (2014), no. 2, 103–115. MR 3274099 |
| Reference:
|
[6] Biçer E., Tunç C.: On the existence of periodic solutions to non-linear neutral differential equations of first order with multiple delays.Proc. of the Pakistan Academy of Sciences 52 (2015), no. 1, 89–94. MR 3413819 |
| Reference:
|
[7] Gabsi H., Ardjouni A., Djoudi A.: Existence of periodic solutions for two types of second-order nonlinear neutral integro-differential equations with infinite distributed mixed-delay.Advances in the Theory of Nonlinear Analysis and Its Applications 2 (2018), no. 4, 184–194. MR 3666594 |
| Reference:
|
[8] Hafsia D.: Existence of periodic solutions for a second order nonlinear integro-differential equations with variable delay.Canad. J. Appl. Math. 2 (2020), no. 1, 36–44. MR 2685037 |
| Reference:
|
[9] Liu Y., Ge W.: Positive periodic solutions of nonlinear Duffing equations with delay and variable coefficients.Tamsui Oxf. J. Math. Sci. 20 (2004), no. 2, 235–255. MR 2108843 |
| Reference:
|
[10] Mansouri B., Ardjouni A., Djoudi A.: Existence of positive periodic solutions for two types of third-order nonlinear neutral differential equations with variable coefficients.Differ. Uravn. Protsessy Upr. 3 (2018), no. 3, 46–63. MR 3866279 |
| Reference:
|
[11] Raffoul Y.: Analysis of periodic and asymptotically periodic solutions in nonlinear coupled Volterra integro-differential systems.Turkish. J. Math. 42 (2018), no. 1, 108–120. MR 3762750, 10.3906/mat-1611-123 |
| Reference:
|
[12] Raffoul Y. N.: Periodic solutions for neutral nonlinear differential equations with functional delay.Electron. J. Differential Equations 2003 (2003), no. 102, 7 pages. MR 2011575 |
| Reference:
|
[13] Smart D. R.: Fixed Point Theorems.Cambridge Tracts in Mathematics, 66, Cambridge University Press, London, 1974. Zbl 0427.47036, MR 0467717 |
| Reference:
|
[14] Wang Y., Lian H., Ge W.: Periodic solutions for a second order nonlinear functional differential equation.Appl. Math. Lett. 20 (2007), no. 1, 110–115. MR 2273618, 10.1016/j.aml.2006.02.028 |
| . |
