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

Youssef Raffoul; Habib Rai

Nonautonomous Dynamical Systems (2016)

  • Volume: 3, Issue: 1, page 14-23
  • ISSN: 2353-0626

Abstract

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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 [...]

How to cite

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Youssef Raffoul, and Habib Rai. "Uniform Stability In Nonlinear Infinite Delay Volterra Integro-differential Equations Using Lyapunov Functionals." Nonautonomous Dynamical Systems 3.1 (2016): 14-23. <http://eudml.org/doc/277109>.

@article{YoussefRaffoul2016,
abstract = {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 [...]},
author = {Youssef Raffoul, Habib Rai},
journal = {Nonautonomous Dynamical Systems},
keywords = {Nonlinear; Volterra; Zero solution; Stability; Infinite delay; Lyapunov functional; nonlinear; zero solution; stability; infinite delay},
language = {eng},
number = {1},
pages = {14-23},
title = {Uniform Stability In Nonlinear Infinite Delay Volterra Integro-differential Equations Using Lyapunov Functionals},
url = {http://eudml.org/doc/277109},
volume = {3},
year = {2016},
}

TY - JOUR
AU - Youssef Raffoul
AU - Habib Rai
TI - Uniform Stability In Nonlinear Infinite Delay Volterra Integro-differential Equations Using Lyapunov Functionals
JO - Nonautonomous Dynamical Systems
PY - 2016
VL - 3
IS - 1
SP - 14
EP - 23
AB - 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 [...]
LA - eng
KW - Nonlinear; Volterra; Zero solution; Stability; Infinite delay; Lyapunov functional; nonlinear; zero solution; stability; infinite delay
UR - http://eudml.org/doc/277109
ER -

References

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  1. [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.  Zbl0058.09401
  2. [2] T. A. Burton, Fixed points and stability of a nonconvolution equation, Proc. Amer. Math. Soc., 132(2004), p.3679-3687.  Zbl1050.34110
  3. [3] T. A. Burton, Stability by fixed point theory or Liapunov theory: A comparison, Fixed Point Theory 4(2003), 15-32.  Zbl1061.47065
  4. [4] T. Burton, Stability by Fixed Point Theory for Functional Differential Equations, Dover Pub,ication, New York, 2006.  Zbl1160.34001
  5. [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. [6] J. Levin, The asymptotic behavior of the solution oa Volterra equation, Proc. Amer. Math. Soc. 14(1963), 534-541. [Crossref] Zbl0115.32403
  7. [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.  Zbl1097.45008
  8. [8] J. Levin and A. Nohel, On a nonlinear delay equations, J. Math. Anal. Appl. 8(1964), 31-44. [Crossref] Zbl0129.07703
  9. [9] A. Nohel, A class of nonlinear delay differential equations, J. Math. Physics 38(1960), 295-311. [Crossref] Zbl0094.08601
  10. [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. [11] T.Wang, Inequalities and stability for a linear scalar functional differential equation, J.Math. Anal. Appl. 298 (2004), 33-44. [Crossref] Zbl1064.34062

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