Periodic Solutions of a Class of Integrodifferential Impulsive Periodic Systems with Time-varying Generating Operators on Banach Space

This paper deals with a class of integrodifferential impulsive periodic systems with time-varying generating operators on Banach space. Using impulsive periodic evolution operator given by us, the suitable T0-periodic PC-mild solution is introduced and Poincaré operator is constructed. Showing the compactness of Poincaré operator and using a new generalized Gronwall’s inequality with impulse, mixed type integral operators and B-norm given by us, we utilize LeraySchauder fixed point theorem to prove the existence of T0-periodic PC-mild solutions. Our method is much different from methods of other papers. At last, an example is given for demonstration.