Existence of periodic solutions for a scalar differential equation modelling optical conveyor belts

TL;DR

This paper investigates a scalar differential equation modeling optical conveyor belts, demonstrating the existence of periodic solutions in specific cases and establishing boundedness of the solution set under general conditions.

Contribution

It provides new existence results for periodic solutions and bounds their set, advancing understanding of the mathematical behavior of optical conveyor belt models.

Findings

Periodic solutions exist in certain physical cases.

The set of periodic solutions is bounded under general assumptions.

The results apply to models of optical conveyor belts.

Abstract

We study a one-dimensional ordinary differential equation modelling optical conveyor belts, showing in particular cases of physical interest that periodic solutions exist. Moreover, under rather general assumptions it is proved that the set of periodic solutions is bounded.