This paper studies the existence and stability of periodic PC-mild solution for the omega-periodic logistic system with T0 -periodic impulsive perturbations on Banach spaces. One sufficient condition with gamma = omega/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 omega and T0 are rational dependent and its period must be nT0 for some n isin N. At last, a numerical example is given for demonstration.
[Show abstract][Hide abstract] ABSTRACT: This paper deals with a class of integrodifferential impulsive periodic systems with time-varying generating operators on Banach space. Using impulsive periodic evolution operator given by us, the suitable T0-periodic PC-mild solution is introduced and Poincare operator is constructed. Showing the compactness of Poincare operator and using a new generalized Gronwall's inequality with impulse, mixed type integral operators and B-norm given by us, we utilize Leray- Schauder fixed point theorem to prove the existence of T0-periodic PC-mild solutions. Our method is much different from methods of other papers. At last, an example is given for demonstration.
Electronic Journal of Qualitative Theory of Differential Equations 01/2009; 2009(4). DOI:10.14232/ejqtde.2009.1.4 · 0.82 Impact Factor
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