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. Our main contribution in this direction is to obtain a continuation theorem for the periodic problem associated with $(\phi(u'))' + \lambda k(t,u,u') = 0$, under the only assumption that $\phi$ is a homeomorphism.
"An application of coincidence degree theory to cyclic feedback type systems associated with nonlinear differential operators." Topol. Methods Nonlinear Anal. 50 (2) 683 - 726, 2017. https://doi.org/10.12775/TMNA.2017.038