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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.

MSC:

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

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