Existence and Global Asymptotical Stability of Periodic Solution for the T-Periodic logistic System with Time-Varying Generating Operators and T0-Periodic Impulsive Perturbations on Banach Spaces

Abstract EN

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 T0-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 T0-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 T0 are rational dependent and its period must be nT0 for some n∈N.

At last, an example is given for demonstration.