Nonautonomous differential relations and their connections with differential equations the right hand side of which is discontinuous with respect to space variables. (English) Zbl 0547.34012

Differential equations and applications, Vol. I, Proc. 2nd Conf., Rousse/Bulg. 1981, 398-404 (1982).
[For the entire collection see Zbl 0476.00012.]
The author studies the differential inclusion \(\dot x\in Q(t,x)\) (\(t\in R\), \(x\in R^ n)\) with compact and convex valued multifunctions in the right-hand side. This equation is used as a tool to define and investigate the notion of a solution to the differential equation \(\dot x=q(t,x)\) with the right-hand side discontinuous in x.
Reviewer: I.Ginchev


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


Zbl 0476.00012