Periodic solutions of integral equations

Summary

A periodic solution of an integral equation is a solution defined on the whole real line that repeats after a fixed period $T > 0$. One looks for such solutions when the data of the equation, its forcing term and its kernel, are themselves $T$-periodic in time. Equations with infinite memory, where the integral runs over the whole past, are the natural setting. Periodic solutions describe the steady oscillations of systems with memory under periodic forcing, much as periodic solutions do for differential equations.