Function bounds for solutions of Volterra integro dynamic equations on time scales

M. Adivar, Izmir University of Economics, Balcova, Izmir, Turkey

E. J. Qualitative Theory of Diff. Equ., No. 7. (2010), pp. 1-22.

Communicated by P. Eloe.Received on 2009-09-23
Appeared on 2010-01-08

Abstract: Introducing shift operators on time scales we construct the integro-dynamic equation corresponding to the convolution type Volterra differential and difference equations in particular cases $\mathbb{T}=\mathbb{R}$ and
$\mathbb{T}=\mathbb{Z}$. Extending the scope of time scale variant of Gronwall's inequality we determine function bounds for the solutions of the integro dynamic equation.

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