Addition to the classical theory of Favard

A study is made of the linear equation p_t = A(t) p +f(t) with an almost periodic matrix A(t) and an almost periodic free termf(t). It is shown that if a bounded solution exists, then an almost periodic solution in the sense of Besicovitch also exists.Translated from Matematicheskie Zametki, Vol. 7, No. 2, pp. 239–246, February, 1970.