Repelling conditions for boundary sets using Lyapunov-like functions. II: Persistence and periodic solutions (Q2640024)

[For part I see Rend. Semin. Mat. Univ. Padova 80, 95-116 (1988; Zbl 0672.34048).] The paper presents repulsivity conditions for the points of the boundary of a set G, with respect to the solutions of the differential system \(x'=f(t,x)\) which are contained in the set G. Applications are given to the problem of ``persistence'' (i.e., solutions starting at the interior of a set remain asymptotically far from its boundary) and to the existence of periodic solutions (using the ``nonejective'' fixed point theorem).