- Research Article
- Open Access
Boundedness in functional dynamic equations on time scales
Advances in Difference Equations volume 2006, Article number: 079689 (2006)
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.
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
Bohner M, Peterson A: Dynamic Equations on Time Scales. An Introduction with Applications. Birkhäuser Boston, Massachusetts; 2001:x+358.
Bohner M, Peterson A (Eds): Advances in Dynamic Equations on Time Scales. Birkhäuser Boston, Massachusetts; 2003:xii+348.
Bohner M, Raffoul YN: Volterra dynamic equations on time scales. preprint
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
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.
Raffoul YN: Boundedness in nonlinear differential equations. Nonlinear Studies 2003,10(4):343–350.
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
About this article
Cite this article
Akin-Bohner, E., Raffoul, Y.N. Boundedness in functional dynamic equations on time scales. Adv Differ Equ 2006, 079689 (2006). https://doi.org/10.1155/ADE/2006/79689
- Differential Equation
- Partial Differential Equation
- Ordinary Differential Equation
- Functional Analysis
- Functional Equation