Asymptotic analysis for Volterra difference equations

Article type: Research Article

Authors: Cuevas, Claudio^; | Choquehuanca, Mario | Soto, Herme

Affiliations: Departamento de Matemática, Universidade Federal de Pernambuco, Recife-PE, CEP 50540-740, Brazil. E-mail: cch@dmat.ufpe.br | Departamento de Matemática y Estadística, Universidad de La Frontera, Casilla 54-D Temuco, Chile. E-mails: {mchoque@ufro.cl, herme.soto@ufrontera.cl}

Note: [] Corresponding author. E-mail: cch@dmat.ufpe.br

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)=λΣj=−∞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.

Keywords: Volterra difference equation, perturbation theory, asymptotic behavior, continuity properties, compactness properties

DOI: 10.3233/ASY-131213

Journal: Asymptotic Analysis, vol. 88, no. 3, pp. 125-164, 2014