On first order multivalued initial and periodic value problems. (English) Zbl 1019.34008

Benchohra, Mouffak; Boucherif, Abdelkader

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)

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