Stability in Retarded Functional Equations

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.

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  • [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