Existence and Global Asymptotical Stability of Periodic Solution for the 7 -Periodic Logistic System with Time-Varying Generating Operators and To-Periodic Impulsive Perturbations on Banach Spaces

摘要

This paper studies the existence and global asymptotical stability of periodic PC-mild solution for the T-periodic logistic system with time-varying generating operators and To-periodic impulsive perturbations on Banach spaces Two sufficient conditions that guarantee the exponential stability of the impulsive evolution operator corresponding to homogenous well-posed T-periodic system with time-varying generating operators and To-periodic impulsive perturbations are given It is shown that the system have a unique periodic PC-mild solution which is globally asymptotically stable when T and TQ are rational dependent and its period must be nTg for some n e N. At last, an example is given for demonstration.