TY - JOUR AU - Feltrin, Guglielmo AU - Zanolin, Fabio PY - 2017/10/28 Y2 - 2024/03/28 TI - An application of coincidence degree theory to cyclic feedback type systems associated with nonlinear differential operators JF - Topological Methods in Nonlinear Analysis JA - TMNA VL - 50 IS - 2 SE - DO - UR - https://apcz.umk.pl/TMNA/article/view/TMNA.2017.038 SP - 683 - 726 AB - 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. ER -