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Existence of Positive Periodic Solutions of First Order Neutral Differential Equations

Year 2023, Volume: 11 Issue: 1, 15 - 19, 30.04.2023

Abstract

In this paper, we consider two classes of first order neutral nonlinear differential equations and we give some new sufficient conditions for the existence of positive periodic solutions of these equations by using the Krasnoselskii's fixed point theorem. An illustrative example is provided to support the theory developed in this study.

References

  • [1] R. P. Agarwal, M. Bohner and W.-T. li, Nonoscillation and Oscillation: Theory for Functional Differential Equations, Marcel Dekker, 2004.
  • [2] T. Candan, Existence of positive periodic solutions of first order neutral differential equations with variable coefficients, Appl. Math. Lett., 52 (2016), 142-148.
  • [3] T. Candan, Existence of positive periodic solutions of first order neutral differential equations, Math. Methods Appl. Sci., 40(1) (2017), 205-209.
  • [4] T. Candan, Existence of positive periodic solution of second-order neutral differential equations, Turkish J. Math., 42(3) (2018), 797–806.
  • [5] J. Dˇzurina, Said R. Grace, Irena Jadlovsk´a and Tongxing Li, Oscillation criteria for second-order Emden-Fowler delay differential equations with a sublinear neutral term, Math. Nachr., 293(5) (2020), 910-922.
  • [6] J. R. Graef and L. Kong, Periodic solutions of first order functional differential equations, Appl. Math. Lett., 24 (2011), 1981-1985.
  • [7] Tongxing Li and Yuriy V. Rogovchenko, Oscillation criteria for second-order superlinear Emden-Fowler neutral differential equations, Monatsh. Math., 184(3) (2017), 489-500.
  • [8] Tongxing Li and Yuriy V. Rogovchenko, On the asymptotic behavior of solutions to a class of third-order nonlinear neutral differential equations, Appl. Math. Lett., 105 (2020), Art. 106293.
  • [9] Z. Li and X. Wang, Existence of positive periodic solutions for neutral functional differential equations, Electron. J. Differential Equations., 34 (2006), 8 pp.
  • [10] Z. Liu, X. Li, S. M. Kang and Y. C. Kwun, Positive periodic solutions for first-order neutral functional differential equations with periodic delays, Abstr. Appl. Anal., (2012), 185692, 12 pp.
  • [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 (2008), 581-587.
  • [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 (2014), 151-162.
  • [13] L. Yao, Global Exponential Convergence of Neutral Type Shunting Inhibitory Cellular Neural Networks with D Operator, Neural Processing Letters, 45 (2017), 401–409.
Year 2023, Volume: 11 Issue: 1, 15 - 19, 30.04.2023

Abstract

References

  • [1] R. P. Agarwal, M. Bohner and W.-T. li, Nonoscillation and Oscillation: Theory for Functional Differential Equations, Marcel Dekker, 2004.
  • [2] T. Candan, Existence of positive periodic solutions of first order neutral differential equations with variable coefficients, Appl. Math. Lett., 52 (2016), 142-148.
  • [3] T. Candan, Existence of positive periodic solutions of first order neutral differential equations, Math. Methods Appl. Sci., 40(1) (2017), 205-209.
  • [4] T. Candan, Existence of positive periodic solution of second-order neutral differential equations, Turkish J. Math., 42(3) (2018), 797–806.
  • [5] J. Dˇzurina, Said R. Grace, Irena Jadlovsk´a and Tongxing Li, Oscillation criteria for second-order Emden-Fowler delay differential equations with a sublinear neutral term, Math. Nachr., 293(5) (2020), 910-922.
  • [6] J. R. Graef and L. Kong, Periodic solutions of first order functional differential equations, Appl. Math. Lett., 24 (2011), 1981-1985.
  • [7] Tongxing Li and Yuriy V. Rogovchenko, Oscillation criteria for second-order superlinear Emden-Fowler neutral differential equations, Monatsh. Math., 184(3) (2017), 489-500.
  • [8] Tongxing Li and Yuriy V. Rogovchenko, On the asymptotic behavior of solutions to a class of third-order nonlinear neutral differential equations, Appl. Math. Lett., 105 (2020), Art. 106293.
  • [9] Z. Li and X. Wang, Existence of positive periodic solutions for neutral functional differential equations, Electron. J. Differential Equations., 34 (2006), 8 pp.
  • [10] Z. Liu, X. Li, S. M. Kang and Y. C. Kwun, Positive periodic solutions for first-order neutral functional differential equations with periodic delays, Abstr. Appl. Anal., (2012), 185692, 12 pp.
  • [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 (2008), 581-587.
  • [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 (2014), 151-162.
  • [13] L. Yao, Global Exponential Convergence of Neutral Type Shunting Inhibitory Cellular Neural Networks with D Operator, Neural Processing Letters, 45 (2017), 401–409.
There are 13 citations in total.

Details

Primary Language English
Subjects Applied Mathematics
Journal Section Articles
Authors

Tuncay Candan

Publication Date April 30, 2023
Submission Date October 18, 2022
Acceptance Date April 24, 2023
Published in Issue Year 2023 Volume: 11 Issue: 1

Cite

APA Candan, T. (2023). Existence of Positive Periodic Solutions of First Order Neutral Differential Equations. Konuralp Journal of Mathematics, 11(1), 15-19.
AMA Candan T. Existence of Positive Periodic Solutions of First Order Neutral Differential Equations. Konuralp J. Math. April 2023;11(1):15-19.
Chicago Candan, Tuncay. “Existence of Positive Periodic Solutions of First Order Neutral Differential Equations”. Konuralp Journal of Mathematics 11, no. 1 (April 2023): 15-19.
EndNote Candan T (April 1, 2023) Existence of Positive Periodic Solutions of First Order Neutral Differential Equations. Konuralp Journal of Mathematics 11 1 15–19.
IEEE T. Candan, “Existence of Positive Periodic Solutions of First Order Neutral Differential Equations”, Konuralp J. Math., vol. 11, no. 1, pp. 15–19, 2023.
ISNAD Candan, Tuncay. “Existence of Positive Periodic Solutions of First Order Neutral Differential Equations”. Konuralp Journal of Mathematics 11/1 (April 2023), 15-19.
JAMA Candan T. Existence of Positive Periodic Solutions of First Order Neutral Differential Equations. Konuralp J. Math. 2023;11:15–19.
MLA Candan, Tuncay. “Existence of Positive Periodic Solutions of First Order Neutral Differential Equations”. Konuralp Journal of Mathematics, vol. 11, no. 1, 2023, pp. 15-19.
Vancouver Candan T. Existence of Positive Periodic Solutions of First Order Neutral Differential Equations. Konuralp J. Math. 2023;11(1):15-9.
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