Asymptotic analysis for Volterra difference equations

Abstract

Let X be an arbitrary Banach space. This work deals with the asymptotic behavior, the continuity and the compactness properties of solutions of the non-linear Volterra difference equation in X described by u(n+1)=λΣ_j=−∞ⁿa(n−j)u(j)+f(n,u(n)), n∈Z, for λ in a distinguished subset of the complex plane, where a(n) is a complex summable sequence and the perturbation f is a non-Lipschitz nonlinearity. Concrete applications to control systems and integro-difference equations are given.