Exponential and l p-Stability in Volterra Equations

Youssef N. Raffoul
Additional contact information
Youssef N. Raffoul: University of Dayton, Department of Mathematics

Chapter Chapter 6 in Qualitative Theory of Volterra Difference Equations, 2018, pp 253-309 from Springer

Abstract: Abstract This chapter is devoted primarily to the exponential and lp-stability of Volterra difference equations. Lyapunov functionals are the main tools in the analysis. It is pointed out that in the case of exponential stability, Lyapunov functionals are hard to extend to vector Volterra difference equations or to Volterra difference equations with infinite delay Infinite delay . In addition, we use nonstandard discretization scheme due to Mickens [122] and apply them to continuous Volterra integro-differential equations. We will show that under the discretization scheme the stability of the zero solution of the continuous dynamical system is preserved. Also, under the same discretization, using a combination of Lyapunov functionals, Laplace transforms, and z-transforms, we show that the boundedness of solutions of the continuous dynamical system is preserved.

Date: 2018
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-97190-2_6

Ordering information: This item can be ordered from
http://www.springer.com/9783319971902

DOI: 10.1007/978-3-319-97190-2_6

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().