Communications in Mathematical Analysis

Exponential Stability in Functional Dynamic Equations On Time Scales

Elvan Akın--Bohner , Youssef N. Raffoul , and Christopher Tisdell

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We are interested in the exponential stability of the zero solution of a functional dynamic equation on a time scale, a nonempty closed subset of real numbers. The approach is based on suitable Lyapunov functionals and certain inequalities. We apply our results to obtain exponential stability in Volterra integrodynamic equations on time scales.

Article information

Commun. Math. Anal., Volume 9, Number 1 (2010), 93-108.

First available in Project Euclid: 21 April 2010

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 39A10

measure chains time scales Lyapunov functionals non-negative definite exponential stability Volterra integro-dynamic equations


Akın--Bohner , Elvan; Raffoul , Youssef N.; Tisdell , Christopher. Exponential Stability in Functional Dynamic Equations On Time Scales. Commun. Math. Anal. 9 (2010), no. 1, 93--108.

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  • M. Ad\ivar and Y. Raffoul, Existence results for periodic solutions of integro-dynamic equations on time scales. Annali di Mathematica, DOI 10.1007/s1023-008-0088-z.
  • S. Bodine and D. A. Lutz, Exponential functions on time scales: Their asymptotic behavior and calculation. Dynam. Systems Appl. 12 (2003), pp 23-43.
  • E. Ak\in-Bohner, M. Bohner and F. Ak\in, Pachpatte inequalities on time scales. JIPAM. J. Inequal. Pure Appl. Math. 6(1) (2005), pp 1-23.
  • E. Ak\in-Bohner, and Y. Raffoul, Boundeness in functional dynamic equations on time scales. Adv. Difference Equ. 2006 2006, pp 1-18.
  • M. Bohner and A. Peterson, Dynamic Equations on Time Scales: An Introduction with Applications, Birkhäuser, Boston, 2001.
  • M. Bohner and A. Peterson, Advances in Dynamic Equations on Time Scales, Birkhäuser, Boston, 2003.
  • M. Bohner and Y. Raffoul, Volterra Dynamic Equations on Time Scales. Preprint.
  • A. Peterson and Y. Raffoul, Exponential stability of dynamic equations on time scales. Adv. Difference Equ. 2 (2005), pp 133-144.
  • A. Peterson and C. C. Tisdell, Boundedness and uniqueness of solutions to dynamic equations on time scales. J. Diff. Equations Appl. 10 No. 13-15 (2004), pp 1295-1306.
  • C. Poetzsche, Chain rule and invariance principle on measure chains. Dynamic equations on time scales. J. Comput. Appl. Math., 141, No. 1-2 (2002), pp 249–254.
  • Y. Raffoul, Boundedness in nonlinear functional differential equations with applications to volterra integrodifferential. J. Integral Equations Appl. 16, No. 4, Winter 2004.
  • Y. Raffoul, Boundedness in Nonlinear Differential Equations. Nonlinear Stud. 10 (2003), pp 343-350.