Weighted Asymptotically Periodic Solutions of Linear Volterra Difference Equations

Abstract EN

A linear Volterra difference equation of the form x(n+1)=a(n)+b(n)x(n)+∑i=0nK(n,i)x(i), where x:N0→R, a:N0→R, K:N0×N0→R and b:N0→R∖{0} is ω-periodic, is considered.

Sufficient conditions for the existence of weighted asymptotically periodic solutions of this equation are obtained.

Unlike previous investigations, no restriction on ∏j=0ω-1b(j) is assumed.

The results generalize some of the recent results.