The influence of bounded external actions on stationary modes in systems with aftereffect (Q5942151)

The authors consider the following system: \[ \dot{X}= AX+\int_{-h}^{0} \,dG(\cdot) X(t_0+\cdot)+ F(\cdot). \] It is proved that the system has a) a unique globally uniformly exponentially stable equilibrium when \(F(\cdot)=F(X(t+\cdot));\) b) a unique globally uniformly exponentially stable \(T\)-periodic and almost periodic solutions when \(F(\cdot)=F(t,X(t+\cdot)).\) Besides, boundedness and existence of \(T\)-periodic and almost periodic solutions are established.