An application of coincidence degree theory to cyclic feedback type systems associated with nonlinear differential operators
Keywords
Cyclic feedback systems, coincidence degree, periodic solutions, continuation theorems, $\phi$-Laplacian operatorsAbstract
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.References
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