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 T-0-periodic PC-mild solution is introduced and Poincare operator is constructed. Showing the compactness of Poincare operator and using a new generalized Gronwall's inequality with impulse, mixed type integral operators and B-norm given by us, we utilize Leray-Schauder fixed point theorem to prove the existence of T-0-periodic PC-mild solutions. Our method is much different from methods of other papers. Atlast, an example is given for demonstration.