Document Type
Post-Print
Publication Date
12-2007
Abstract
We show that the condition |a| + |∑+∞l=0bl| < 1 is not necessary, though sufficient, for the asymptotic stability of xn+1 = axn + ∑+∞l=0bn-lxl. We prove the existence of a class of Volterra difference equations (VDEs) that violate this condition but whose zero solutions are asymptotically stable.
Identifier
10.1080/10236190701264529
Publisher
Taylor & Francis
Repository Citation
Elaydi, S., Messina, E., & Vecchio, A. (2007). On the asymptotic stability of linear Volterra difference equations of convolution type. Journal of Difference Equations and Applications, 13(12), 1079-1084. doi:10.1080/10236190701264529
Publication Information
Journal of Difference Equations and Applications