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STABILITY CRITERIA FOR RETARDED FUNCTIONAL DIFFERENTIAL EQUATIONS

Year 2020, Volume: 8 Issue: 2, 212 - 222, 31.08.2020
https://doi.org/10.20290/estubtdb.625933

Abstract


In this work, we examine the stability behavior of retarded functional differential equations. The asymptotic behavior of solutions and stability of the zero solution are investigated by using a suitable real root for the characteristic equation. Three examples are also given to illustrate our results.


In this work, we examine the stability behavior of retarded functional differential equations. The asymptotic behavior of solutions and stability of the zero solution are investigated by using a suitable real root for the characteristic equation. Three examples are also given to illustrate our results.



In this work, we examine the stability behavior of retarded functional differential equations. The asymptotic behavior of solutions and stability of the zero solution are investigated by using a suitable real root for the characteristic equation. Three examples are also given to illustrate our results.

References

  • [1] K.L. Cooke and J.M. Ferreira, Stability Conditions for Linear Retarded Functional Differential Equations, Journal of Mathematical Analysis and Applications, 96, 480-504 (1983).
  • [2] J.M. Ferreira and I. Györi, Oscillatory Behavior in Linear Retarded Functional Differential Equations, Journal of Mathematical Analysis and Applications, 128, 332-346 (1987).
  • [3] A.M. Pedro, Oscillation and nonoscillation criteria for retarded functional differential equations, Proceedings of Equadiff-11, 2005, pp.353–362.
  • [4] A.M. Pedro, Nonoscillation criteria for retarded functional differential systems, International Journal of Pure and Applied Mathematics, Volume 31 No. 1 2006, 47-71.
  • [5] A.M. Pedro, Oscillation criteria for retarded functional differential systems, International Journal of Pure and Applied Mathematics, Volume 63 No. 1 2010, 75-84.
  • [6] J.K. Hale and S.M. Verduyn Lunel, Introduction to Functional Differential Equations, Springer, Berlin, Heidelberg, New York, 1993.
  • [7] H. d’Albis, E. Augeraud-Véron and H.J. Hupkes, Multiple solutions in systems of functional differential equations, Journal of Mathematical Economics, 52 (2014) 50–56.
  • [8] Q. Kong, Oscillation for Systems of Functional Differential Equations, Journal of Mathematical Analysis and Applications, 198, 608-619 (1996).
  • [9] Ch. G. Philos and I. K. Purnaras, Asymptotic properties, nonoscillation, and stability for scalar first order linear autonomous neutral delay differential equations, Electron. J. Differential Equations, 2004 (2004), No. 03, pp. 1-17.
  • [10] T.A. Burton, Volterra Integral and Differential Equations, Academic Press, New York, (1983).
  • [11] C. Corduneanu, Integral Equations and Applications, Cambridge University Press, New York, (1991).
  • [12] V. Kolmanovski, A. Myshkis, Applied Theory of Functional Differential Equations, Kluver Academic, Dordrecht, 1992.
  • [13] Y. Kuang, Delay Differential Equations with Applications in Population Dynamics, Academic Press, San Diego, 1993.
  • [14] V. Lakshmikantham, L. Wen, and B. Zhang, Theory of Differential Equations with Unbounded Delay, Kluwer Academic Publishers, London, 1994.
  • [15] S.-I. Niculescu, Delay Effects on Stability, Springer-Verlag London Limited, 2001.
  • [16] N.J. Ford, Y. Yan, Md.A. Malique, Numerical treatment of oscillatory functional differential equations, Journal of Computational and Applied Mathematics, 234 (2010) 2757–2767.
  • [17] Md. A. Malique, Numerical treatment of oscillatory delay and mixed functional differential equations arising in modeling, University of Liverpool (University of Chester), Unpublished doctoral dissertation, 2012.
  • [18] I.-G. E. Kordonis, N. T. Niyianni and 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.
  • [19] I.-G.E. Kordonis and Ch.G. Philos, The Behavior of solutions of linear integro-differential equations with unbounded delay, Computers & Mathematics with Applications, 38 (1999) 45-50.
  • [20] Ch.G. Philos and I.K. Purnaras, Periodic first order linear neutral delay differential equatiıons, Applied Mathematics and Computation,117 (2001) 203-22

STABILITY CRITERIA FOR RETARDED FUNCTIONAL DIFFERENTIAL EQUATIONS

Year 2020, Volume: 8 Issue: 2, 212 - 222, 31.08.2020
https://doi.org/10.20290/estubtdb.625933

Abstract

In
this work, we examine the stability behavior of the retarded functional
differential equation. The asymptotic behavior of solutions and stability of
the zero solution are investigated by using a suitable real root for
characteristic equation. Three examples are also given to illustrate our
results.



In this work, we examine the stability behavior of retarded functional differential equations. The asymptotic behavior of solutions and stability of the zero solution are investigated by using a suitable real root for the characteristic equation. Three examples are also given to illustrate our results. 



In this work, we examine the stability behavior of retarded functional differential equations. The asymptotic behavior of solutions and stability of the zero solution are investigated by using a suitable real root for the characteristic equation. Three examples are also given to illustrate our results.

References

  • [1] K.L. Cooke and J.M. Ferreira, Stability Conditions for Linear Retarded Functional Differential Equations, Journal of Mathematical Analysis and Applications, 96, 480-504 (1983).
  • [2] J.M. Ferreira and I. Györi, Oscillatory Behavior in Linear Retarded Functional Differential Equations, Journal of Mathematical Analysis and Applications, 128, 332-346 (1987).
  • [3] A.M. Pedro, Oscillation and nonoscillation criteria for retarded functional differential equations, Proceedings of Equadiff-11, 2005, pp.353–362.
  • [4] A.M. Pedro, Nonoscillation criteria for retarded functional differential systems, International Journal of Pure and Applied Mathematics, Volume 31 No. 1 2006, 47-71.
  • [5] A.M. Pedro, Oscillation criteria for retarded functional differential systems, International Journal of Pure and Applied Mathematics, Volume 63 No. 1 2010, 75-84.
  • [6] J.K. Hale and S.M. Verduyn Lunel, Introduction to Functional Differential Equations, Springer, Berlin, Heidelberg, New York, 1993.
  • [7] H. d’Albis, E. Augeraud-Véron and H.J. Hupkes, Multiple solutions in systems of functional differential equations, Journal of Mathematical Economics, 52 (2014) 50–56.
  • [8] Q. Kong, Oscillation for Systems of Functional Differential Equations, Journal of Mathematical Analysis and Applications, 198, 608-619 (1996).
  • [9] Ch. G. Philos and I. K. Purnaras, Asymptotic properties, nonoscillation, and stability for scalar first order linear autonomous neutral delay differential equations, Electron. J. Differential Equations, 2004 (2004), No. 03, pp. 1-17.
  • [10] T.A. Burton, Volterra Integral and Differential Equations, Academic Press, New York, (1983).
  • [11] C. Corduneanu, Integral Equations and Applications, Cambridge University Press, New York, (1991).
  • [12] V. Kolmanovski, A. Myshkis, Applied Theory of Functional Differential Equations, Kluver Academic, Dordrecht, 1992.
  • [13] Y. Kuang, Delay Differential Equations with Applications in Population Dynamics, Academic Press, San Diego, 1993.
  • [14] V. Lakshmikantham, L. Wen, and B. Zhang, Theory of Differential Equations with Unbounded Delay, Kluwer Academic Publishers, London, 1994.
  • [15] S.-I. Niculescu, Delay Effects on Stability, Springer-Verlag London Limited, 2001.
  • [16] N.J. Ford, Y. Yan, Md.A. Malique, Numerical treatment of oscillatory functional differential equations, Journal of Computational and Applied Mathematics, 234 (2010) 2757–2767.
  • [17] Md. A. Malique, Numerical treatment of oscillatory delay and mixed functional differential equations arising in modeling, University of Liverpool (University of Chester), Unpublished doctoral dissertation, 2012.
  • [18] I.-G. E. Kordonis, N. T. Niyianni and 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.
  • [19] I.-G.E. Kordonis and Ch.G. Philos, The Behavior of solutions of linear integro-differential equations with unbounded delay, Computers & Mathematics with Applications, 38 (1999) 45-50.
  • [20] Ch.G. Philos and I.K. Purnaras, Periodic first order linear neutral delay differential equatiıons, Applied Mathematics and Computation,117 (2001) 203-22
There are 20 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Ali Fuat Yeniçerioğlu 0000-0002-1063-0538

Cüneyt Yazıcı 0000-0002-4535-510X

Publication Date August 31, 2020
Published in Issue Year 2020 Volume: 8 Issue: 2

Cite

APA Yeniçerioğlu, A. F., & Yazıcı, C. (2020). STABILITY CRITERIA FOR RETARDED FUNCTIONAL DIFFERENTIAL EQUATIONS. Eskişehir Teknik Üniversitesi Bilim Ve Teknoloji Dergisi B - Teorik Bilimler, 8(2), 212-222. https://doi.org/10.20290/estubtdb.625933
AMA Yeniçerioğlu AF, Yazıcı C. STABILITY CRITERIA FOR RETARDED FUNCTIONAL DIFFERENTIAL EQUATIONS. Eskişehir Teknik Üniversitesi Bilim ve Teknoloji Dergisi B - Teorik Bilimler. August 2020;8(2):212-222. doi:10.20290/estubtdb.625933
Chicago Yeniçerioğlu, Ali Fuat, and Cüneyt Yazıcı. “STABILITY CRITERIA FOR RETARDED FUNCTIONAL DIFFERENTIAL EQUATIONS”. Eskişehir Teknik Üniversitesi Bilim Ve Teknoloji Dergisi B - Teorik Bilimler 8, no. 2 (August 2020): 212-22. https://doi.org/10.20290/estubtdb.625933.
EndNote Yeniçerioğlu AF, Yazıcı C (August 1, 2020) STABILITY CRITERIA FOR RETARDED FUNCTIONAL DIFFERENTIAL EQUATIONS. Eskişehir Teknik Üniversitesi Bilim ve Teknoloji Dergisi B - Teorik Bilimler 8 2 212–222.
IEEE A. F. Yeniçerioğlu and C. Yazıcı, “STABILITY CRITERIA FOR RETARDED FUNCTIONAL DIFFERENTIAL EQUATIONS”, Eskişehir Teknik Üniversitesi Bilim ve Teknoloji Dergisi B - Teorik Bilimler, vol. 8, no. 2, pp. 212–222, 2020, doi: 10.20290/estubtdb.625933.
ISNAD Yeniçerioğlu, Ali Fuat - Yazıcı, Cüneyt. “STABILITY CRITERIA FOR RETARDED FUNCTIONAL DIFFERENTIAL EQUATIONS”. Eskişehir Teknik Üniversitesi Bilim ve Teknoloji Dergisi B - Teorik Bilimler 8/2 (August 2020), 212-222. https://doi.org/10.20290/estubtdb.625933.
JAMA Yeniçerioğlu AF, Yazıcı C. STABILITY CRITERIA FOR RETARDED FUNCTIONAL DIFFERENTIAL EQUATIONS. Eskişehir Teknik Üniversitesi Bilim ve Teknoloji Dergisi B - Teorik Bilimler. 2020;8:212–222.
MLA Yeniçerioğlu, Ali Fuat and Cüneyt Yazıcı. “STABILITY CRITERIA FOR RETARDED FUNCTIONAL DIFFERENTIAL EQUATIONS”. Eskişehir Teknik Üniversitesi Bilim Ve Teknoloji Dergisi B - Teorik Bilimler, vol. 8, no. 2, 2020, pp. 212-2, doi:10.20290/estubtdb.625933.
Vancouver Yeniçerioğlu AF, Yazıcı C. STABILITY CRITERIA FOR RETARDED FUNCTIONAL DIFFERENTIAL EQUATIONS. Eskişehir Teknik Üniversitesi Bilim ve Teknoloji Dergisi B - Teorik Bilimler. 2020;8(2):212-2.