No abstract

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.Mathematics Subject Classification. 34K30, 34K45, 35R12, 47D06.Keywords. First-order abstract Cauchy problem, impulsive differential equations, mild solutions, asymptotically periodic solutions, strongly continuous semigroups of linear operators.

No abstract

No abstract