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Boundedness in functional dynamic equations on time scales

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Using nonnegative definite Lyapunov functionals, we prove general theorems for the boundedness of all solutions of a functional dynamic equation on time scales. We apply our obtained results to linear and nonlinear Volterra integro-dynamic equations on time scales by displaying suitable Lyapunov functionals.



  1. 1.

    Akın-Bohner E, Bohner M, Akın F: Pachpatte inequalities on time scales. Journal of Inequalities in Pure and Applied Mathematics 2005,6(1):1–23. article 6

  2. 2.

    Bohner M, Peterson A: Dynamic Equations on Time Scales. An Introduction with Applications. Birkhäuser Boston, Massachusetts; 2001:x+358.

  3. 3.

    Bohner M, Peterson A (Eds): Advances in Dynamic Equations on Time Scales. Birkhäuser Boston, Massachusetts; 2003:xii+348.

  4. 4.

    Bohner M, Raffoul YN: Volterra dynamic equations on time scales. preprint

  5. 5.

    Peterson AC, Raffoul YN: Exponential stability of dynamic equations on time scales. Advances in Difference Equations 2005,2005(2):133–144. 10.1155/ADE.2005.133

  6. 6.

    Peterson AC, Tisdell CC: Boundedness and uniqueness of solutions to dynamic equations on time scales. Journal of Difference Equations and Applications 2004,10(13–15):1295–1306.

  7. 7.

    Raffoul YN: Boundedness in nonlinear differential equations. Nonlinear Studies 2003,10(4):343–350.

  8. 8.

    Raffoul YN: Boundedness in nonlinear functional differential equations with applications to Volterra integrodifferential equations. Journal of Integral Equations and Applications 2004,16(4):375–388. 10.1216/jiea/1181075297

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Correspondence to Elvan Akin-Bohner.

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  • Differential Equation
  • Partial Differential Equation
  • Ordinary Differential Equation
  • Functional Analysis
  • Functional Equation