Criteria for the Response of Nonlinear Systems to be L-Asymptotically Periodic

2359 periodic with a given period r, and q has finite energy?f This type of question arises naturally in many applications. Our results are basically "tool theorems" which appear to be widely applicable. An example is given in Section 3.4. To provide motivation for considering an abstract input-output operator G, and also to describe some earlier results related to those of Section III, we begin by recalling that an important example of a type of equation that arises in the study of physical systems (such as feedback systems or networks containing linear lumped and/or distributed elements, as well as memoryless, possibly time-varying, nonlinear elements) is the integral equation (1)