Monotone Iterative Technique Of Periodic Solutions For Impulsive Evolution Equations In Banach Space

Based on the theory of semigroups, the paper discussed the existence ofω-periodicmild solutions for impulsive evolution equationsin Banach spaces and the main results are as follows:1.We obtain the existence and uniqueness, denotation of mild solutions and positive solutions for linear impulsive evolution equation by some describing condition of the growth index of semigroup.2. Under impulsive function satisfied the increase order , we discuss the existence results ofω-periodic mild solutions for impulsive evolution equation by using the monotone iterative technique. We extend the results from without impulse to with impulse.3.Under wide monotone conditions and without assumption that the lower and upper solutions are exist, we investigate the existence results ofω-periodic mild solutions for impulsive evolution equation applying the monotone iterative technique. Applied A—0, even for impulsive ordinary differential equations, the results are new.4.Applications to the boundary value problems for the impulsive parabolic partial differential equations, we obtain the existence results ofω-periodic classical solutions.