Existence And Stability Of Periodic Solution For Periodic Logistic System With Periodic Impulsive Perturbations
This paper studies the existence and stability of periodic PC-mild solution for the omega-periodic logistic system with T<sub>0</sub> -periodic impulsive perturbations on Banach spaces. One sufficient condition with gamma = omega/T<sub>0</sub> 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 omega and T<sub>0</sub> are rational dependent and its period must be nT<sub>0</sub> for some n isin N. At last, a numerical example is given for demonstration.
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