Abstract
This paper studies the existence and stability of periodic PC-mild solution for the ω−periodic Logistic system with T0−periodic impulsive perturbations on Banach spaces. One sufficient condition with γ=ω/T0 is rational that guarantees the exponential stability of the impulsive evolution operator which is given. It is shown that the system has a unique periodic PC-mild solution which is globally asymptotically stable when ω and T0 are rational dependent and its period must be nT0 for some n∈N. At last, a numerical example is given for demonstration.