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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.

##### MSC:
 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