Stability and Boundedness

Youssef N. Raffoul
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Youssef N. Raffoul: University of Dayton, Department of Mathematics

Chapter Chapter 1 in Qualitative Theory of Volterra Difference Equations, 2018, pp 1-54 from Springer

Abstract: Abstract In this chapter we provide a brief introduction to difference calculus including basic material on Volterra difference equations. Using the z-transform we state some known theorems regarding stability of the zero solution of Volterra difference equations of convolution types. We move on to introducing Lyapunov functions for autonomous difference equations and state some known results concerning stability and boundedness. In Section 1.3 we introduce the concept of total stability and its correlation with uniform asymptotic stability for perturbed Perturbed Volterra difference equations.

Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-97190-2_1

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DOI: 10.1007/978-3-319-97190-2_1

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