Partial averaging for impulsive differential equations with supremum.
In this paper, we consider periodic solutions for a class of nonlinear evolution equations with non-instantaneous impulses on Banach spaces. By constructing a Poincaré operator, which is a composition of the maps and using the techniques of a priori estimate, we avoid assuming that periodic solution is bounded like in [1-4] and try to present new sufficient conditions on the existence of periodic mild solutions for such problems by utilizing semigroup theory and Leray-Schauder's fixed point theorem....
In this paper, for the impulsive fractional integro-differential equations involving Caputo fractional derivative in Banach space, we investigate the existence and uniqueness of a pseudo almost periodic -mild solution. The working tools are based on the fixed point theorems, the fractional powers of operators and fractional calculus. Some known results are improved and generalized. Finally, existence and uniqueness of a pseudo almost periodic -mild solution of a two-dimensional impulsive fractional...