On linear homogeneous almost periodic systems that satisfy the Favard condition

We prove the existence of a linear homogeneous almost periodic system of differential equations that has nontrivial bounded solutions and is such that all systems from a certain neighborhood of it have no nontrivial almost periodic solutions. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 3. pp. 409–413, March, 1998.