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

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...

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Bibliographic Details
Published in:Electronic journal of qualitative theory of differential equations 2010, Vol.2010 (7), p.1-22
Main Author: Adivar, Murat
Format: Article
Language:English
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Summary: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.
ISSN:1417-3875
1417-3875
DOI:10.14232/ejqtde.2010.1.7