PERIODIC SOLUTIONS AND STABILITY OF LINEAR EVOLUTION EQUATIONS WITH NONINSTANTANEOUS IMPULSES

摘要

This paper concerns existence and stability of solutions to periodic linear evolution equations with noninstantaneous impulses via the theory of operator semigroup. A series of fundamental results including compactness, semigroup property, exponential estimate and periodicity are established for a new introduced impulsive evolution operator. Moreover, triple sufficient conditions are given to guarantee this impulsive evolution operator is exponentially stable. In addition, a relationship between existence of periodic solutions and fixed point of impulsive evolution operator is determined, and the alternative results on periodic solutions and their asymptotical stability are obtained by using the well known Fredholm alternative theorem. Finally, an example of periodic impulsive parabolic linear partial differential equation is given for illustration of the theoretically results.