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Asymptotic behavior of solutions of discrete Volterra equations

Migda J, Migda M.

Opuscula Mathematica

2016

Vol. 36, no. 2

265--278

We consider the nonlinear discrete Volterra equations of non-convolution type [formula] We present sufficient conditions for the existence of solutions with prescribed asymptotic behavior, especially asymptotically polynomial and asymptotically periodic solutions. We use o(ns), for a given nonpositive real s, as a measure of approximation. We also give conditions under which all solutions are asymptotically polynomial.

On Exponential Stability of Volterra Difference Equations with Infinite Delay

Ngoc P. H. A., Hieu L. T.

Bulletin of the Polish Academy of Sciences. Mathematics

2014

Vol. 62, no 2

125--137

General nonlinear Volterra difference equations with infinite delay are considered. A new explicit criterion for global exponential stability is given. Furthermore, we present a stability bound for equations subject to nonlinear perturbations. Two examples are given to illustrate the results obtained.

On asymptotically periodic solutions of linear discrete Volterra equations

Győri I., Reynolds D. W.

Fasciculi Mathematici

2010

Nr 44

53-67

We show that a class of linear nonconvolution discrete Volterra equations has asymptotically periodic solutions. We also examine an example for which the calculations can be done explicitly. The results are established using theorems on the boundedness and convergence to a finite limit of solutions of linear discrete Volterra equations.