Existence and Global Asymptotical Stability of Periodic Solution for theT-Periodic Logistic System with Time-Varying Generating Operators andT0-Periodic Impulsive Perturbations on Banach Spaces

JinRong Wang, X. Xiang, W. Wei, Qian Chen
2008 Discrete Dynamics in Nature and Society  
This paper studies the existence and global asymptotical stability of periodic PC-mild solution for theT-periodic Logistic system with time-varying generating operators andT0-periodic impulsive perturbations on Banach spaces. Two sufficient conditions that guarantee the exponential stability of the impulsive evolution operator corresponding to homogenous well-posedT-periodic system with time-varying generating operators andT0-periodic impulsive perturbations are given. It is shown that the
more » ... m have a unique periodic PC-mild solution which is globally asymptotically stable whenTandT0are rational dependent and its period must benT0for somen∈N. At last, an example is given for demonstration.
doi:10.1155/2008/524945 fatcat:ors5fmqcyjb3boyb4xheug4xym