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

• Autorzy: Youssef Raffoul , Habib Rai
• 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 [...]

Słowa kluczowe

EN

Nonlinear; Volterra; Zero solution; Stability; Infinite delay; Lyapunov functional

• Wydawca: De Gruyter Open
• Czasopismo: Nonautonomous Dynamical Systems
• Rocznik: 2016
• Tom: 3
• Numer: 1
• Strony: 14-23

Daty

otrzymano

2015-11-12

zaakceptowano

2016-02-18

online

2016-05-02

Twórcy

autor

Youssef Raffoul

• Department of Mathematics, University of Dayton, Dayton, OH 45469-2316

autor

Habib Rai

• Department of Mechanical Engineering, University of Balamand, Koura, Lebanon

Bibliografia

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• [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]

Identyfikatory

DOI

10.1515/msds-2016-0002