Existence results for positive periodic solutions to first order neutral differential equations with distributed deviating arguments

Year 2024, Volume: 53 Issue: 5, 1326 - 1332, 15.10.2024

Tuncay Candan

https://doi.org/10.15672/hujms.1282490

Abstract

We take into account the first order nonlinear neutral differential equation with distributed deviating arguments. Using Krasnoselskii's fixed point theorem, we give some new criteria for the existence of positive periodic solutions to this equation. The theorems we have established are illustrated by an example.

Keywords

fixed point, distributed delay, neutral equations, positive periodic solution, first-order

References

• [1] T. Candan, Oscillation behavior of solutions for even order neutral functional differential equations, Appl. Math. Mech. (English Ed.) 27, 1311–1320, 2006.
• [2] T. Candan, Existence of positive periodic solutions of first order neutral differential equations with variable coefficients, Appl. Math. Lett. 52, 142–148, 2016.
• [3] T. Candan, Existence of positive periodic solutions of first order neutral differential equations, Math. Methods Appl. Sci. 40(1), 205–209, 2017.
• [4] T. Candan, Existence of positive periodic solution of second-order neutral differential equations, Turkish J. Math. 42(3), 797–806, 2018.
• [5] J. Durina, S. R. Grace, I. Jadlovská and T. Li, Oscillation criteria for second-order Emden-Fowler delay differential equations with a sublinear neutral term, Math. Nachr. 293(5), 910–922, 2020.
• [6] J. R. Graef and L. Kong, Periodic solutions of first order functional differential equations, Appl. Math. Lett. 24, 1981-1985, 2011.
• [7] T. Li and Y. V. Rogovchenko, Oscillation criteria for second-order superlinear Emden-Fowler neutral differential equations, Monatsh. Math. 184(3), 489–500, 2017.
• [8] T. Li and Y. V. Rogovchenko, On the asymptotic behavior of solutions to a class of third-order nonlinear neutral differential equations, Appl. Math. Lett. 105, Art. 106293, 2020.
• [9] Z. Li and X. Wang, Existence of positive periodic solutions for neutral functional differential equations, Electron. J. Differ. Equ. 34, 8 pp, 2006.
• [10] Z. Liu, X. Li, S. M. Kang and Y. C. Kwun, Positive periodic solutions for firstorder neutral functional differential equations with periodic delays, Abstr. Appl. Anal., 185692, 12 pp, 2012.
• [11] Y. Luo, W. Wang and J. Shen, Existence of positive periodic solutions for two kinds of neutral functional differential equations, Appl. Math. Lett. 21, 581-587, 2008.
• [12] M. B. Mesmouli, A. Ardjouni and A. Djoudi, Positive periodic solutions for first-order nonlinear neutral functional differential equations with periodic delay, Transylv. J. Math. Mech. 6, 151-162, 2014.
• [13] Y. N Raffoul, Existence of positive periodic solutions in neutral nonlinear equations with functional delay, Rocky Mountain J. Math. 42(6), 19831993, 2012.
• [14] Y. N Raffoul, M. Ünal, Boundedness, Periodic Solutions and Stability in Neutral Functional Delay Equations with Application to Bernoulli Type Differential Equations, Commun. Appl. Anal. 19, 149162, 2015.