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On first order multivalued initial and periodic value problems. (English) Zbl 1019.34008
The authors study the existence of solutions to first-order differential inclusions of the form \(y'(t)\in F(t,y(t)) \) a.e. \(t\in [0,T],\) with initial (\(y(0)=a\)) or periodic (\(y(0)=y(T)\)) condition, where \(F: [0,T]\times \mathbb{R}\to \mathbb{R}\) is a closed, bounded and convex-valued multivalued map. They convert the problem to an appropriate fixed-point problem and use a fixed-point theorem for condensing maps combined with upper and lower solutions.

34A60 Ordinary differential inclusions
34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
34C25 Periodic solutions to ordinary differential equations