About the behavior of solutions for Volterra difference equations with infinite delay

Abstract

We study the existence of discrete almost automorphic solutions and asymptotic behavior for non-linear Volterra difference equations of convolution type with infinite delay where the nonlinear perturbation is considered not necessarily globally Lipschitz. The results are a consequence of application of different fixed point theorems, namely, the contraction principle, the Leray–Schauder, the Krasnoselkii and Matkowski’s fixed point technique.