Existence of bounded solutions of retarded functional differential equations

This article is devoted to questions about existence of solutions of system s of retarded functional differential equations (y)over dot(t) = f(t, yt) w ith a graph remaining on its right maximal interval of existence in some op en region. A topological technique of (n,p,z)-subsets for investigation of these questions is developed. An application concerning existence of bounde d solutions of an equation of second order is given.