Bifurcation of periodic solutions in differential inclusions. (English) Zbl 0903.34036

A general system of inclusions \[ \dot x(t) \in f(x(t))+\sum_{j=1}^k \mu_j f_j(x(t), \mu,t), \] \(x: \mathbb{R} \to \mathbb{R}^n\) is considered, where \(f, f_j\) are compact- and convex-valued upper semicontinuous mappings and \(\mu = (\mu_1, \dots, \mu_k)\) is a parameter. Assuming that the structure of the set of \(1\)-periodic solutions for \(\mu = 0\) is known, the author applies topological degree theory for multivalued mappings to give sufficient conditions for the existence of bifurcating \(1\)-periodic solutions for \(\mu \) close to \(0\). It is shown that systems involving both static and dynamic dry friction terms belong to this class.


34C25 Periodic solutions to ordinary differential equations
34A60 Ordinary differential inclusions
34C23 Bifurcation theory for ordinary differential equations
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