Smoothness property on parameters of periodic systems

Correspondence: [email protected] Kent State University at Trumbull, Warren, OH 44483, USA Abstract This work is concerned with periodic systems dependent on parameters and investigates differentiability with respect to parameters of the periodic solutions of the systems. Some challenging situations arise from a hyperbolic type of periodic boundary value problem. Using some auxiliary operators and applying semigroup theory and a fixed point theorem, we are able to handle these cases and obtain the results on the existence and differentiability with respect to parameters of periodic solutions. The application of the obtained abstract results to a periodic boundary value problem is discussed at the end of the article. AMS Subject Classification: 47D62; 45K05; 35L20.