# zbMATH — the first resource for mathematics

Topological degree and periodic solutions of differential inclusions. (English) Zbl 0936.34009
In this interesting paper, the authors study the existence of periodic solutions to differential inclusions of the form $x'(t)\in F(t,x(t)),\quad x(a)= x(0),\tag{Q$$_F$$}$ where $$F$$ is a multivalued map. Under an assumption on the existence of some guiding potentials for $$F$$ and other reasonable conditions, they prove that the problem $$(Q_F)$$ has a solution. The proof is based on a new topological degree theory for the corresponding Poincaré map of $$(Q_F)$$.
Another interesting result in this paper is a construction of this new topological degree theory. Based upon this theory, the authors put the study of $$(Q_F)$$ with $$F$$ convex- or nonconvex-valued in a unitary setting. This new topological degree theory may be applied to other problems.
Reviewer: Bin Liu (Beijing)

##### MSC:
 34A60 Ordinary differential inclusions 34C25 Periodic solutions to ordinary differential equations
Full Text: