Multiple slowly oscillating periodic solutions for x'(t) = f(x(t-1)) with negative feedback

TL;DR

This paper investigates the existence and characteristics of slowly oscillating periodic solutions in a delayed negative feedback differential equation, reviewing known results and presenting new findings and examples.

Contribution

It provides new results and examples on the existence and nonuniqueness of slowly oscillating periodic solutions in the prototype delay differential equation.

Findings

Review of known results on solution uniqueness

Presentation of new solutions and examples

Insights into nonuniqueness of solutions

Abstract

We consider the prototype equation x'(t) = f(x(t-1)) for delayed negative feedback. We review known results on uniqueness and nonuniqueness of slowly oscillating periodic solutions, and present some new results and examples.