## 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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