Periodic perturbations with delay of coupled differential equations on manifolds with application to a sunflower-like equation

TL;DR

This paper studies the existence of periodic solutions in coupled delay differential equations on manifolds, using topological methods, and applies these results to a generalized sunflower equation.

Contribution

It introduces a fixed point index and degree-theoretic approach to establish periodic solutions for perturbed coupled delay differential equations on manifolds, including a novel application to sunflower-like equations.

Findings

Existence of branches of T-periodic solutions proved.

Application to a generalized sunflower equation demonstrated.

Topological methods effectively analyze delay differential equations on manifolds.

Abstract

We investigate the structure of the set of $T$-periodic solutions to periodically perturbed coupled delay differential equations on differentiable manifolds. By using fixed point index and degree-theoretic methods we prove the existence of branches of $T$-periodic solutions to the considered equations. As main application of our methods, we study a generalized version of the sunflower equation.