Luis del Campo, Manuel Pinto, Claudio Vidal: Bounded and periodic solutions for abstract functional difference equations with summable dichotomies: Applications to Volterra systems, 279-292

Abstract:

Using the existence of summable dichotomies in linear functional difference equations, the Contraction Principle and the Schauder Fixed Point Theorem, we obtain the existence of bounded and periodic solutions under quite general hypotheses for nonlinear functional difference equations on phase spaces. Applications of our main results to Volterra equations are given. Moreover, examples are also given to illustrate obtained results.

Key Words: Retarded functional difference equations; Phase spaces; Discrete summable dichotomies; Bounded solutions; Contraction fixed point theorem; Schauder fixed point theorem; Volterra difference equations.

2010 Mathematics Subject Classification: Primary 34C27, 43A60. Secondary 35B15, 34K30, 34G20.