Global Solutions for Abstract Differential Equations with Non-Instantaneous Impulses

In this note we study the existence of global solutions for a class of impulsive abstract differential equations with non-instantaneous impulses. Specifically, we establish the existence of mild solutions on [ 0 , ∞) and the existence of S-asymptotically ω-periodic mild solutions. Our results are based on the Hausdorff measure of non-compactness. Some applications involving partial differential equations are considered. © 2015, Springer Basel.