New comparison results for impulsive integro-differential equations and applications. (English) Zbl 1113.45007
The authors study a nonlinear first-order impulsive integro-differential equation with periodic boundary value conditions. They established some new comparison principles for ordinary integro-differential equations and then introduce new definitions for lower and upper solutions of the considered boundary value problem. Based on the existence of such solutions, the existence of a solution to the periodic boundary value problem is proved, as well as the existence of two sequences that converge uniformly to the extremal solutions of this problem. The two sequences are between the lower and upper solutions. The paper ends with some illustrative examples for the new results.
Reviewer: Iulian Stoleriu (Heidelberg)
Keywords:
maximum principle; impulsive integro-differential equation; periodic boundary value problem; upper and lower solution; monotone methodReferences:
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