Consider , , the continuous function , the continuous functions , , , the set ; , the functions , and the functions
Suppose that there exist the limits
and denote , .
The authors consider the first-order impulsive integrodifferential equation
with periodic boundary value conditions
and prove some comparison principles and establish existence results for extremal solutions of the problem using these principles and the monotone iterative technique.
For example, they consider the Banach spaces and , where
with the norms , respectively, and if there exist the functions and in , , satisfying some hypotheses, then there exist monotone sequences , of functions with
which converge uniformly on to the extremal solutions of the problem in