Qualitative theory for Volterra difference equations

In this paper, we show the existence of function which is not S-asymptotically ω-periodic, but which is S-asymptotically ω-periodic in the Stepanov sense. We give sufficient conditions for the existence and uniqueness of S-asymptotically ω-periodic solutions for a nonautonomous differential equation with piecewise constant argument in a Banach space when ω is an integer. This is done using the Banach fixed point Theorem. An example involving the heat operator is discussed as an illustration of the theory.

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Qualitative theory for Volterra difference equations

Abstract: We investigate lp boundedness, the topological structure of solutions set and the asymptotic periodicity of Volterra functional difference equations. The theoretical results are complemented with a set of applications.

Cited by 4 publications

References 38 publications

Pseudo Antiperiodic Solutions to Volterra Difference Equations

Pseudo Antiperiodic Solutions to Volterra Difference Equations

Discrete Subdiffusion Equations with Memory

Pseudo S-asymptotically ω-periodic solution for a differential equation with piecewise constant argument in a Banach space

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