Periodic boundary value problems for a class of second-order impulsive integro-differential equations in Banach spaces. (English) Zbl 0889.45016

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.
Reviewer: Eduardo Liz (Vigo)


45N05 Abstract integral equations, integral equations in abstract spaces
45J05 Integro-ordinary differential equations
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