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2016 | 3 | 1 | 14-23
Tytuł artykułu

Uniform Stability In Nonlinear Infinite Delay Volterra Integro-differential Equations Using Lyapunov Functionals

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In [10] the first author used Lyapunov functionals and studied the exponential stability of the zero solution of finite delay Volterra Integro-differential equation. In this paper, we use modified version of the Lyapunov functional that were used in [10] to obtain criterion for the stability of the zero solution of the infinite delay nonlinear Volterra integro-differential equation [...]
Wydawca
Rocznik
Tom
3
Numer
1
Strony
14-23
Opis fizyczny
Daty
otrzymano
2015-11-12
zaakceptowano
2016-02-18
online
2016-05-02
Twórcy
  • Department of Mathematics, University of Dayton, Dayton, OH 45469-2316
autor
  • Department of Mechanical Engineering, University of Balamand, Koura, Lebanon
Bibliografia
  • [1] H. Brown and K. Ergen, A theoremon rearrangements and its application to certain delay differential equations, J. Rat. Mech. Anal. 3(1954), 565-579.
  • [2] T. A. Burton, Fixed points and stability of a nonconvolution equation, Proc. Amer. Math. Soc., 132(2004), p.3679-3687.
  • [3] T. A. Burton, Stability by fixed point theory or Liapunov theory: A comparison, Fixed Point Theory 4(2003), 15-32.
  • [4] T. Burton, Stability by Fixed Point Theory for Functional Differential Equations, Dover Pub,ication, New York, 2006.
  • [5] M. Cable and Y. Raffoul, Exponential stability and instability in multiple delays differential equations, International Journal of Mathematics Sciences and Applications, Vol. 1. No. 2 (May 2011).
  • [6] J. Levin, The asymptotic behavior of the solution oa Volterra equation, Proc. Amer. Math. Soc. 14(1963), 534-541. [Crossref]
  • [7] M. N. Islam and Y. N. Raffoul, Stability in Linear Volterra Integrodifferential equations with nonlinear perturbation, Journal of Integral Equations and Applications, Volume 17, Number 3, Fall 2005, 259-276.
  • [8] J. Levin and A. Nohel, On a nonlinear delay equations, J. Math. Anal. Appl. 8(1964), 31-44. [Crossref]
  • [9] A. Nohel, A class of nonlinear delay differential equations, J. Math. Physics 38(1960), 295-311. [Crossref]
  • [10] Y. Raffoul, Exponential Stability and Instability in Finite Delay nonlinear Volterra Integro-differential Equations, Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis 20 (2013) 95-106.
  • [11] T.Wang, Inequalities and stability for a linear scalar functional differential equation, J.Math. Anal. Appl. 298 (2004), 33-44. [Crossref]
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_1515_msds-2016-0002
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