An application of coincidence degree theory to cyclic feedback type systems associated with nonlinear differential operators

TL;DR

This paper applies Mawhin's coincidence degree theory to establish new continuation theorems for cyclic feedback systems, facilitating the analysis of periodic solutions in nonlinear differential equations with applications to vector ODEs involving the -Laplacian operator.

Contribution

It introduces novel continuation theorems using coincidence degree theory specifically tailored for cyclic feedback systems with nonlinear differential operators.

Findings

New continuation theorems for cyclic feedback systems

Application to vector ODEs with -Laplacian operators

Examples demonstrating the theorems' effectiveness

Abstract

Using Mawhin's coincidence degree theory, we obtain some new continuation theorems which are designed to have as a natural application the study of the periodic problem for cyclic feedback type systems. We also discuss some examples of vector ordinary differential equations with a $\phi$-Laplacian operator where our results can be applied.