Stability of difference Volterra equations: Direct Liapunov method and numerical procedure

Boundedness and Asymptotic Stability for the Solution of Homogeneous Volterra Discrete Equations

“…It is well known that one of the most used tools in the stability analysis of VDEs is the Lyapunov approach [22][23][24][25][26][27][28]. As already mentioned in the introduction, among the results that can be obtained by Lyapunov techniques, the most popular are based on the hypothesis that the coefficients are summable (e.g., the result in [28,Th.…”

Some stability conditions for scalar Volterra difference equations

“…For example, the boundedness of solutions of discrete Volterra equations was studied in [2,5,10] or [13]- [18], the periodicity was investigated in papers [6,8,15,18]. A survey of the fundamental results on the stability of linear Volterra difference equations, of both convolution and non-convolution type, can be found in [7], see also [3,4,11,12,17] or [19]. In [3] and [4] the authors study the exponential stability of equation…”

“…A survey of the fundamental results on the stability of linear Volterra difference equations, of both convolution and non-convolution type, can be found in [7], see also [3,4,11,12,17] or [19]. In [3] and [4] the authors study the exponential stability of equation…”

Estimates for the norms of solutions of difference systems with several delays

“…For this latter trend, see Zhang and Chen [12], Crisci et al [4], Lakshmikantham and Trigiante [7], and Agarwal and Wong [2]. By this method many very strong results are obtained.…”