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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
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