Benchohra, Mouffak; Boucherif, Abdelkader On first order multivalued initial and periodic value problems. (English) Zbl 1019.34008 Dyn. Syst. Appl. 9, No. 4, 559-568 (2000). 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. Reviewer: S.K.Ntouyas (Ioannina) Cited in 4 Documents 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 Keywords:differential inclusion; initial value problems; periodic solutions PDF BibTeX XML Cite \textit{M. Benchohra} and \textit{A. Boucherif}, Dyn. Syst. Appl. 9, No. 4, 559--568 (2000; Zbl 1019.34008) OpenURL