Department of Mathematics, University of Dayton, Dayton, OH, 45469-2316
Using Schaefer's fixed-point theorem, enabling us to show that if there is an a priori bound on all possible T-periodic solutions of an infinite delay Volterra difference equation, then there is a T-periodic solution. We apply our results to scalar infinite delay Volterra difference equations in which, the a priori bound is established by means of non-negative definite Lyapunov functionals.
A priori bound, infinite delay equations, periodic solutions, Schaefer's fixed-point theorem, Lyapunov functionals
