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Year 2021, Volume: 4 Issue: 1, 33 - 40, 22.03.2021

Ali Fuat Yeniçerioğlu Cüneyt Yazıcı Vildan Yazıcı

https://doi.org/10.32323/ujma.711881

Abstract

References

  • [1] T.A. Burton, Volterra integral and differential equations, Academic Press, New York, 1983.
  • [2] K.L. Cooke, J.M. Ferreira, Stability conditions for linear retarded functional differential equations, J. Math. Anal. Appl., 96 (1983), 480–504.
  • [3] C. Corduneanu, Integral equations and applications, Cambridge University Press, New York, 1991.
  • [4] J.M. Ferreira, I. Gy¨or˙I, Oscillatory behavior in linear retarded functional differential equations, J. Math. Anal. Appl., 128 (1987), 332–346.
  • [5] J.M. Ferreira, A.M. Pedro, Oscillations of differential-difference systems of neutral type, J. Math. Anal. Appl., 253 (2001), 274–289.
  • [6] J.M. Ferreira, A.M. Pedro, Oscillatory behaviour in functional differential systems of neutral type, J. Math. Anal. Appl., 269 (2002), 533–555.
  • [7] N.J. Ford, Y. Yan, Md.A. Malique, Numerical treatment of oscillatory functional differential equations, J. of Comput. and Appl. Math., 234 (2010), 2757–2767.
  • [8] J.K. Hale, S.M. Verduyn Lunel, Introduction to functional differential equations, Springer, Berlin, Heidelberg, New York, 1993.
  • [9] V.B. Kolmanovskii, V.R. Nosov, Stability of functional differential equations, Academic Press, Inc., London, 1986.
  • [10] V.B. Kolmanovskii, A. Myshkis, Applied theory of functional differential equations, Kluver Academic, Dordrecht, 1992.
  • [11] Q. Kong, Oscillation for systems of functional differential equations, J. Math. Anal. Appl., 198 (1996), 608–619.
  • [12] I.G. E. Kordonis, N. T. Niyianni, Ch. G. Philos, On the behavior of the solutions of scalar first order linear autonomous neutral delay differential equations, Arch. Math. (Basel), 71 (1998), 454–464.
  • [13] I.G.E. Kordonis, Ch.G. Philos, The behavior of solutions of linear integro-differential equations with unbounded delay, Comput. Math. Appl., 38 (1999), 45–50.
  • [14] Y. Kuang, Delay differential equations with applications in population dynamics, Academic Press, San Diego, 1993.
  • [15] V. Lakshmikantham, L. Wen, B. Zhang, Theory of differential equations with unbounded delay, Kluwer Academic Publishers, London, 1994.
  • [16] K. Leffler, The Riemann-Stieltjes integral and some applications in complex analysis and probability theory. Umea University, Institutionen f¨or matematik och matematisk statistik, 2014.
  • [17] Md. A. Malique, Numerical treatment of oscillatory delay and mixed functional differential equations arising in modeling, PhD thesis, University of Liverpool (University of Chester), 2012.
  • [18] S.I. Niculescu, Delay effects on stability, Springer-Verlag London Limited, 2001.
  • [19] A.M. Pedro, Oscillation and nonoscillation criteria for retarded functional differential equations, in: International Conference on Differential Equations (Proc. Internat. Sympos., Czecho-Slovak series, Bratislava, 2005), Comenius University Press, Bratislava, (2007), 353–362.
  • [20] A.M. Pedro, Nonoscillation criteria for retarded functional differential systems, Inter. J. of Pure and Appl. Math., 31 (2006), 47–71.
  • [21] A.M. Pedro, Oscillation criteria for retarded functional differential systems, Inter. J. of Pure and Appl. Math., 63 (2010), 75–84.
  • [22] Ch.G. Philos, I.K. Purnaras, Periodic first order linear neutral delay differential equations, Appl. Math. Comput., 117 (2001), 203–222.
  • [23] Ch.G. Philos, I.K. Purnaras, Asymptotic properties, nonoscillation, and stability for scalar first order linear autonomous neutral delay differential equations, Electron. J. Differential Equations, 03 (2004), 1–17.
  • [24] Ch.G. Philos, I.K. Purnaras, More on the behavior of solutions to linear integro differantial equations with unbounded delay, Funkcial. Ekvac., 48 (2005), 393–414.
  • [25] Ch.G. Philos, I.K. Purnaras, A result on the behavior of the solutions for scalar first order linear autonomous neutral delay differential equations, Math. Proc. Camb. Phil. Soc., 140 (2006), 349–358.
  • [26] U. Stroinski, Order and oscillation in delay differential systems, J. Math. Anal. Appl., 207 (1997), 158–171.
  • [27] A.F. Yenic¸erioglu, C. Yazıcı, Stability criteria for retarded functional differential equations. Eskis¸ehir Technical Univ. J. of Sci. and Tech. B – Theo.Sci., 8(2), (2020), 212 – 222

Stability Behaviour in Functional Differential Equations of the Neutral Type

Year 2021, Volume: 4 Issue: 1, 33 - 40, 22.03.2021

Ali Fuat Yeniçerioğlu Cüneyt Yazıcı Vildan Yazıcı

https://doi.org/10.32323/ujma.711881

Abstract

In this study, we examine the behavior of solutions of the neutral functional differential equations. Using a suitable real root of the corresponding characteristic equation, the asymptotic behavior of the solutions and the stability of the trivial solution are explained. Three examples are also provided to illustrate our results.

Keywords

Asymptotic behavior Functional differential equation Neutral Characteristic equation Stability

References

  • [1] T.A. Burton, Volterra integral and differential equations, Academic Press, New York, 1983.
  • [2] K.L. Cooke, J.M. Ferreira, Stability conditions for linear retarded functional differential equations, J. Math. Anal. Appl., 96 (1983), 480–504.
  • [3] C. Corduneanu, Integral equations and applications, Cambridge University Press, New York, 1991.
  • [4] J.M. Ferreira, I. Gy¨or˙I, Oscillatory behavior in linear retarded functional differential equations, J. Math. Anal. Appl., 128 (1987), 332–346.
  • [5] J.M. Ferreira, A.M. Pedro, Oscillations of differential-difference systems of neutral type, J. Math. Anal. Appl., 253 (2001), 274–289.
  • [6] J.M. Ferreira, A.M. Pedro, Oscillatory behaviour in functional differential systems of neutral type, J. Math. Anal. Appl., 269 (2002), 533–555.
  • [7] N.J. Ford, Y. Yan, Md.A. Malique, Numerical treatment of oscillatory functional differential equations, J. of Comput. and Appl. Math., 234 (2010), 2757–2767.
  • [8] J.K. Hale, S.M. Verduyn Lunel, Introduction to functional differential equations, Springer, Berlin, Heidelberg, New York, 1993.
  • [9] V.B. Kolmanovskii, V.R. Nosov, Stability of functional differential equations, Academic Press, Inc., London, 1986.
  • [10] V.B. Kolmanovskii, A. Myshkis, Applied theory of functional differential equations, Kluver Academic, Dordrecht, 1992.
  • [11] Q. Kong, Oscillation for systems of functional differential equations, J. Math. Anal. Appl., 198 (1996), 608–619.
  • [12] I.G. E. Kordonis, N. T. Niyianni, Ch. G. Philos, On the behavior of the solutions of scalar first order linear autonomous neutral delay differential equations, Arch. Math. (Basel), 71 (1998), 454–464.
  • [13] I.G.E. Kordonis, Ch.G. Philos, The behavior of solutions of linear integro-differential equations with unbounded delay, Comput. Math. Appl., 38 (1999), 45–50.
  • [14] Y. Kuang, Delay differential equations with applications in population dynamics, Academic Press, San Diego, 1993.
  • [15] V. Lakshmikantham, L. Wen, B. Zhang, Theory of differential equations with unbounded delay, Kluwer Academic Publishers, London, 1994.
  • [16] K. Leffler, The Riemann-Stieltjes integral and some applications in complex analysis and probability theory. Umea University, Institutionen f¨or matematik och matematisk statistik, 2014.
  • [17] Md. A. Malique, Numerical treatment of oscillatory delay and mixed functional differential equations arising in modeling, PhD thesis, University of Liverpool (University of Chester), 2012.
  • [18] S.I. Niculescu, Delay effects on stability, Springer-Verlag London Limited, 2001.
  • [19] A.M. Pedro, Oscillation and nonoscillation criteria for retarded functional differential equations, in: International Conference on Differential Equations (Proc. Internat. Sympos., Czecho-Slovak series, Bratislava, 2005), Comenius University Press, Bratislava, (2007), 353–362.
  • [20] A.M. Pedro, Nonoscillation criteria for retarded functional differential systems, Inter. J. of Pure and Appl. Math., 31 (2006), 47–71.
  • [21] A.M. Pedro, Oscillation criteria for retarded functional differential systems, Inter. J. of Pure and Appl. Math., 63 (2010), 75–84.
  • [22] Ch.G. Philos, I.K. Purnaras, Periodic first order linear neutral delay differential equations, Appl. Math. Comput., 117 (2001), 203–222.
  • [23] Ch.G. Philos, I.K. Purnaras, Asymptotic properties, nonoscillation, and stability for scalar first order linear autonomous neutral delay differential equations, Electron. J. Differential Equations, 03 (2004), 1–17.
  • [24] Ch.G. Philos, I.K. Purnaras, More on the behavior of solutions to linear integro differantial equations with unbounded delay, Funkcial. Ekvac., 48 (2005), 393–414.
  • [25] Ch.G. Philos, I.K. Purnaras, A result on the behavior of the solutions for scalar first order linear autonomous neutral delay differential equations, Math. Proc. Camb. Phil. Soc., 140 (2006), 349–358.
  • [26] U. Stroinski, Order and oscillation in delay differential systems, J. Math. Anal. Appl., 207 (1997), 158–171.
  • [27] A.F. Yenic¸erioglu, C. Yazıcı, Stability criteria for retarded functional differential equations. Eskis¸ehir Technical Univ. J. of Sci. and Tech. B – Theo.Sci., 8(2), (2020), 212 – 222
There are 27 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Ali Fuat Yeniçerioğlu 0000-0002-1063-0538

Cüneyt Yazıcı

Vildan Yazıcı

Publication Date March 22, 2021
Submission Date November 30, 2019
Acceptance Date March 1, 2021
Published in Issue Year 2021 Volume: 4 Issue: 1

Cite

APA Yeniçerioğlu, A. F., Yazıcı, C., & Yazıcı, V. (2021). Stability Behaviour in Functional Differential Equations of the Neutral Type. Universal Journal of Mathematics and Applications, 4(1), 33-40. https://doi.org/10.32323/ujma.711881
AMA Yeniçerioğlu AF, Yazıcı C, Yazıcı V. Stability Behaviour in Functional Differential Equations of the Neutral Type. Univ. J. Math. Appl. March 2021;4(1):33-40. doi:10.32323/ujma.711881
Chicago Yeniçerioğlu, Ali Fuat, Cüneyt Yazıcı, and Vildan Yazıcı. “Stability Behaviour in Functional Differential Equations of the Neutral Type”. Universal Journal of Mathematics and Applications 4, no. 1 (March 2021): 33-40. https://doi.org/10.32323/ujma.711881.
EndNote Yeniçerioğlu AF, Yazıcı C, Yazıcı V (March 1, 2021) Stability Behaviour in Functional Differential Equations of the Neutral Type. Universal Journal of Mathematics and Applications 4 1 33–40.
IEEE A. F. Yeniçerioğlu, C. Yazıcı, and V. Yazıcı, “Stability Behaviour in Functional Differential Equations of the Neutral Type”, Univ. J. Math. Appl., vol. 4, no. 1, pp. 33–40, 2021, doi: 10.32323/ujma.711881.
ISNAD Yeniçerioğlu, Ali Fuat et al. “Stability Behaviour in Functional Differential Equations of the Neutral Type”. Universal Journal of Mathematics and Applications 4/1 (March 2021), 33-40. https://doi.org/10.32323/ujma.711881.
JAMA Yeniçerioğlu AF, Yazıcı C, Yazıcı V. Stability Behaviour in Functional Differential Equations of the Neutral Type. Univ. J. Math. Appl. 2021;4:33–40.
MLA Yeniçerioğlu, Ali Fuat et al. “Stability Behaviour in Functional Differential Equations of the Neutral Type”. Universal Journal of Mathematics and Applications, vol. 4, no. 1, 2021, pp. 33-40, doi:10.32323/ujma.711881.
Vancouver Yeniçerioğlu AF, Yazıcı C, Yazıcı V. Stability Behaviour in Functional Differential Equations of the Neutral Type. Univ. J. Math. Appl. 2021;4(1):33-40.
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