Viable and periodic solutions for differential inclusions in Banach spaces. (English) Zbl 0674.34014

The paper proves several existence theorems for differential inclusion defined on a closed subset of a Banach space. A solution of such differential inclusion is known as a “viable trajectory”. Those results are proved using a tangential condition of Nagumo type. Then the viability results are used to establish the existence of periodic trajectories.
Reviewer: G.Osipenko


34A60 Ordinary differential inclusions
34C25 Periodic solutions to ordinary differential equations
34G10 Linear differential equations in abstract spaces
34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations