Araştırma Makalesi
BibTex RIS Kaynak Göster

Stability in Retarded Functional Equations

Yıl 2022, Cilt: 10 Sayı: 1, 108 - 111, 15.04.2022

Cüneyt Yazıcı Ali Fuat Yeniçerioğlu

Öz

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.

Anahtar Kelimeler

Characteristic equation Retarded equation Stability Trivial solution

Kaynakça

  • [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

Yıl 2022, Cilt: 10 Sayı: 1, 108 - 111, 15.04.2022

Cüneyt Yazıcı Ali Fuat Yeniçerioğlu

Öz

Kaynakça

  • [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
Toplam 20 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Articles
Yazarlar

Cüneyt Yazıcı 0000-0002-4535-510X

Ali Fuat Yeniçerioğlu 0000-0002-1063-0538

Yayımlanma Tarihi 15 Nisan 2022
Gönderilme Tarihi 19 Haziran 2020
Kabul Tarihi 22 Mart 2022
Yayımlandığı Sayı Yıl 2022 Cilt: 10 Sayı: 1

Kaynak Göster

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. Nisan 2022;10(1):108-111.
Chicago Yazıcı, Cüneyt, ve Ali Fuat Yeniçerioğlu. “Stability in Retarded Functional Equations”. Konuralp Journal of Mathematics 10, sy. 1 (Nisan 2022): 108-11.
EndNote Yazıcı C, Yeniçerioğlu AF (01 Nisan 2022) Stability in Retarded Functional Equations. Konuralp Journal of Mathematics 10 1 108–111.
IEEE C. Yazıcı ve A. F. Yeniçerioğlu, “Stability in Retarded Functional Equations”, Konuralp J. Math., c. 10, sy. 1, ss. 108–111, 2022.
ISNAD Yazıcı, Cüneyt - Yeniçerioğlu, Ali Fuat. “Stability in Retarded Functional Equations”. Konuralp Journal of Mathematics 10/1 (Nisan 2022), 108-111.
JAMA Yazıcı C, Yeniçerioğlu AF. Stability in Retarded Functional Equations. Konuralp J. Math. 2022;10:108–111.
MLA Yazıcı, Cüneyt ve Ali Fuat Yeniçerioğlu. “Stability in Retarded Functional Equations”. Konuralp Journal of Mathematics, c. 10, sy. 1, 2022, ss. 108-11.
Vancouver Yazıcı C, Yeniçerioğlu AF. Stability in Retarded Functional Equations. Konuralp J. Math. 2022;10(1):108-11.
 Kapak Resmi İndir
Creative Commons License
The published articles in KJM are licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.