Nonlinear Volterra integral equations and the Schröder functional equation

We show an interesting connection between a special class of Volterra integral equations and the famous Schröder equation. The basic results provide criteria for the existence of nontrivial as well as blow-up solutions of the Volterra equation, expressed in terms of the convergence of some integrals. Examples related to Volterra equations with power and exponential nonlinearities are presented.