Periodic boundary value problems for a class of second-order impulsive integro-differential equations in Banach spaces (Q1378697)

The paper deals with a periodic boundary value problem for a second order nonlinear integro-differential equation with impulses at fixed moments in a Banach space. The concepts of lower and upper solutions for this problem are introduced and then the monotone iterative method is used to construct a couple of monotone sequences converging to the extremal solutions of the problem in a sector defined by a lower solution \(u_{0}\) and an upper solution \(v_{0}\), with \(u_{0}\leq v_{0}\). For it, the authors first study a periodic boundary value problem for a linear impulsive integro-differential equation and prove a comparison result.