On the set of harmonic solutions of a class of perturbed coupled and nonautonomous differential equations on manifolds

TL;DR

This paper investigates the existence and continuation of periodic solutions in a class of perturbed coupled nonautonomous differential equations on manifolds, using degree theory to establish global results.

Contribution

It provides a novel degree-theoretic approach to analyze the global continuation of periodic solutions in perturbed coupled differential equations on manifolds.

Findings

Established a global continuation theorem for T-periodic solutions

Applied degree theory to coupled nonautonomous equations on manifolds

Provided conditions for the existence of periodic solutions

Abstract

We study the set of $T$-periodic solutions of a class of $T$-periodically perturbed coupled and nonautonomous differential equations on manifolds. By using degree-theoretic methods we obtain a global continuation result for the $T$-periodic solutions of the considered equations.