Almost periodic solutions for a certain class of almost periodic systems

Abstract

Using a result due to Medvedev [3], we obtain conditions under which systems of ordinary differential equations of the form x ′ = F ( t , x , x ) + G ( t , x ) x’ = F(t,x,x) + G(t,x) where F F and G G are almost periodic in t t will have unique almost periodic solutions with certain global stability properties and module containment. These conditions are compared to conditions for the existence, but not uniqueness, for such solutions obtained by Kartsatos in [2]. Both results, our as well as Kartsatos’, are applied to a second order equation of Lienard type with almost periodic forcing.