## On periodic solutions, in a given set, for differential systems.(English)Zbl 0725.34039

The existence of periodic solutions of the differential system $$x'=f(t,x)$$, which remain in a given set M is proved. The set M is a piece of a convex set lying between two level surfaces of a Lyapunov-like function. In one example considered the convex cone is $${\mathcal R}^ m$$ and M is the part of the cone which is situated between two spheres. The theory exploits the fixed point index combined with suitable geometric conditions concerning the behaviour of f on the boundary of M.
Reviewer: P.Smith (Keele)

### MSC:

 34C25 Periodic solutions to ordinary differential equations 34C11 Growth and boundedness of solutions to ordinary differential equations 34D40 Ultimate boundedness (MSC2000)