Research Article
BibTex RIS Cite

Stability in Retarded Functional Equations

Year 2022, Volume: 10 Issue: 1, 108 - 111, 15.04.2022

Cüneyt Yazıcı Ali Fuat Yeniçerioğlu

Abstract

This article deals with the stability behavior of a scalar linear retarded equation. Useful exponential estimations and stability criteria of the solutions were established. Finally, two examples are given for the stability of the zero solution of the retarded equation.

Keywords

Characteristic equation Retarded equation Stability Trivial solution

References

  • [1] J.K. Hale and S.M. Verduyn Lunel, Introduction to Functional Differential Equations, Springer, Berlin, Heidelberg, New York, 1993.
  • [2] J.M. Ferreira, Oscillations and Nonoscillations in Retarded Equations, Portugaliae Mathematica, 58, (2001), 127-138.
  • [3] J.M. Ferreira and S. Pinelas, Oscillatory retarded functional systems, J. Math. Anal. Appl., 285, (2003), 506-527.
  • [4] J.M. Ferreira and S. Pinelas, Nonoscillations in retarded systems, J. Math. Anal. Appl., 308, (2005), 714-729.
  • [5] S. Pinelas, Nonoscillations in retarded equations, in: Proc. Int. Conf. Dynamical Systems and Applications, July 5-10, 2004, Antalya, Turkey, submitted for publication.
  • [6] T.A. Burton, Volterra Integral and Differential Equations, Academic Press, New York, 1983.
  • [7] C. Corduneanu, Integral Equations and Applications, Cambridge University Press, New York, 1991).
  • [8] V. Kolmanovski, A. Myshkis, Applied Theory of Functional Differential Equations, Kluver Academic, Dordrecht, 1992.
  • [9] Y. Kuang, Delay Differential Equations with Applications in Population Dynamics, Academic Press, San Diego, 1993.
  • [10] V. Lakshmikantham, L. Wen, and B. Zhang, Theory of Differential Equations with Unbounded Delay, Kluwer Academic Publishers, London, 1994.
  • [11] S.-I. Niculescu, Delay Effects on Stability, Springer-Verlag London Limited, 2001.
  • [12] R. Boucekkine, D. de la Croix and O. Licandro, Vintage human capital, demographic trends, and endogenous growth, Journal. of Economic Theory, 104, (2002), 340-375.
  • [13] D. de la Croix and O. Licandro, Life expectancy and endogenous growth, Economic Letters, 65, (1999), 255-263.
  • [14] H. d’Albis, E. Augeraud-V´eron and H.J. Hupkes, Multiple solutions in systems of functional differential equations, Journal of Mathematical Economics, 52, (2014), 50-56.
  • [15] R. D. Driver, Some harmless delays, Delay and Functional Differential Equations and Their Applications, Academic Press, New York, 1972, pp. 103-119.
  • [16] M. Pituk, Cesaro Summability in a Linear Autonomous Difference Equation, Proceedings of the American Mathematical Society, 133(11), (2005), 3333-3339.
  • [17] 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.
  • [18] 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.
  • [19] Ch.G. Philos and I.K. Purnaras, Periodic first order linear neutral delay differential equations, Applied Mathematics and Computation, 117, (2001), 203-222.
  • [20] 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

Year 2022, Volume: 10 Issue: 1, 108 - 111, 15.04.2022

Cüneyt Yazıcı Ali Fuat Yeniçerioğlu

Abstract

References

  • [1] J.K. Hale and S.M. Verduyn Lunel, Introduction to Functional Differential Equations, Springer, Berlin, Heidelberg, New York, 1993.
  • [2] J.M. Ferreira, Oscillations and Nonoscillations in Retarded Equations, Portugaliae Mathematica, 58, (2001), 127-138.
  • [3] J.M. Ferreira and S. Pinelas, Oscillatory retarded functional systems, J. Math. Anal. Appl., 285, (2003), 506-527.
  • [4] J.M. Ferreira and S. Pinelas, Nonoscillations in retarded systems, J. Math. Anal. Appl., 308, (2005), 714-729.
  • [5] S. Pinelas, Nonoscillations in retarded equations, in: Proc. Int. Conf. Dynamical Systems and Applications, July 5-10, 2004, Antalya, Turkey, submitted for publication.
  • [6] T.A. Burton, Volterra Integral and Differential Equations, Academic Press, New York, 1983.
  • [7] C. Corduneanu, Integral Equations and Applications, Cambridge University Press, New York, 1991).
  • [8] V. Kolmanovski, A. Myshkis, Applied Theory of Functional Differential Equations, Kluver Academic, Dordrecht, 1992.
  • [9] Y. Kuang, Delay Differential Equations with Applications in Population Dynamics, Academic Press, San Diego, 1993.
  • [10] V. Lakshmikantham, L. Wen, and B. Zhang, Theory of Differential Equations with Unbounded Delay, Kluwer Academic Publishers, London, 1994.
  • [11] S.-I. Niculescu, Delay Effects on Stability, Springer-Verlag London Limited, 2001.
  • [12] R. Boucekkine, D. de la Croix and O. Licandro, Vintage human capital, demographic trends, and endogenous growth, Journal. of Economic Theory, 104, (2002), 340-375.
  • [13] D. de la Croix and O. Licandro, Life expectancy and endogenous growth, Economic Letters, 65, (1999), 255-263.
  • [14] H. d’Albis, E. Augeraud-V´eron and H.J. Hupkes, Multiple solutions in systems of functional differential equations, Journal of Mathematical Economics, 52, (2014), 50-56.
  • [15] R. D. Driver, Some harmless delays, Delay and Functional Differential Equations and Their Applications, Academic Press, New York, 1972, pp. 103-119.
  • [16] M. Pituk, Cesaro Summability in a Linear Autonomous Difference Equation, Proceedings of the American Mathematical Society, 133(11), (2005), 3333-3339.
  • [17] 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.
  • [18] 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.
  • [19] Ch.G. Philos and I.K. Purnaras, Periodic first order linear neutral delay differential equations, Applied Mathematics and Computation, 117, (2001), 203-222.
  • [20] 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
There are 20 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Cüneyt Yazıcı 0000-0002-4535-510X

Ali Fuat Yeniçerioğlu 0000-0002-1063-0538

Publication Date April 15, 2022
Submission Date June 19, 2020
Acceptance Date March 22, 2022
Published in Issue Year 2022 Volume: 10 Issue: 1

Cite

APA Yazıcı, C., & Yeniçerioğlu, A. F. (2022). Stability in Retarded Functional Equations. Konuralp Journal of Mathematics, 10(1), 108-111.
AMA Yazıcı C, Yeniçerioğlu AF. Stability in Retarded Functional Equations. Konuralp J. Math. April 2022;10(1):108-111.
Chicago Yazıcı, Cüneyt, and Ali Fuat Yeniçerioğlu. “Stability in Retarded Functional Equations”. Konuralp Journal of Mathematics 10, no. 1 (April 2022): 108-11.
EndNote Yazıcı C, Yeniçerioğlu AF (April 1, 2022) Stability in Retarded Functional Equations. Konuralp Journal of Mathematics 10 1 108–111.
IEEE C. Yazıcı and A. F. Yeniçerioğlu, “Stability in Retarded Functional Equations”, Konuralp J. Math., vol. 10, no. 1, pp. 108–111, 2022.
ISNAD Yazıcı, Cüneyt - Yeniçerioğlu, Ali Fuat. “Stability in Retarded Functional Equations”. Konuralp Journal of Mathematics 10/1 (April 2022), 108-111.
JAMA Yazıcı C, Yeniçerioğlu AF. Stability in Retarded Functional Equations. Konuralp J. Math. 2022;10:108–111.
MLA Yazıcı, Cüneyt and Ali Fuat Yeniçerioğlu. “Stability in Retarded Functional Equations”. Konuralp Journal of Mathematics, vol. 10, no. 1, 2022, pp. 108-11.
Vancouver Yazıcı C, Yeniçerioğlu AF. Stability in Retarded Functional Equations. Konuralp J. Math. 2022;10(1):108-11.
 Download Cover Image
Creative Commons License
The published articles in KJM are licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.