On almost periodic solutions of a class of differential equations

Abstract

A set E of real numbers is called relatively dense if there exists a positive real number I such that every interval of length 1 contains at least one member of the set E. Following Tornehave [4], a continuous function x(t), defined for all real t and having values in a metric space (X, d), is called an almost periodic movement in X if to each positive real number e there corresponds a relatively dense set of real numbers r such that