The existence of almost periodic solutions and periodic solutions (Q807808)

The paper uses the very near connection between the stability and the existence of a periodic or almost periodic solution for a differential system. One of the main results is the following: if the system \(\dot x=f(t,x)\) is periodic and the solution \(x=x(t,x_ 0)\) is uniformly stable with respect to \(\Omega_ x\), then there exists an almost periodic solution.