Periodic perturbations of a class of scalar second order functional differential equations

TL;DR

This paper investigates periodic solutions in a class of second order functional differential equations with delay, using topological methods and a linear chain trick to analyze the effects of periodic perturbations.

Contribution

It introduces a novel topological approach combined with a linear chain trick to study forced oscillations in delay-type functional differential equations.

Findings

Existence of T-periodic solutions under certain conditions

Application of a linear chain trick to reduce the problem

Analysis of delay effects on oscillatory behavior

Abstract

We study, by means of a topological approach, the forced oscillations of second order functional retarded differential equations subject to periodic perturbations. We consider a delay-type functional dependence involving a gamma probability distribution. By a linear chain trick we obtain a first order system of ODE's whose $T$-periodic solutions correspond to those of the functional equation.