Forced periodic oscillations and almost linear behavior

There are considered systems with sector restricted and globally Lipschitz nonlinear functions which are forced by periodic or almost periodic signals. For these systems there is discussed existence, uniqueness and exponential stability of the limit regimes which are of the same type as the forcing term. The three properties considered together define the almost linear behavior. Since partial results may be obtained using stability multipliers, there are analyzed the properties associated to such multipliers and possible extensions. The paper ends with a sketch of a future research programme.