Monotone method for first- and second-order periodic boundary value problems and periodic solutions of functional differential equations. (English) Zbl 1014.34049

The paper is devoted to develop a monotone iterative technique for some first- and second-order periodic boundary value problems for functional-differential equations (FDEs), assuming the existence of a couple of lower and upper solutions. For it, the authors prove some comparison results (maximum principles), following the ideas in [E. Liz and J. J. Nieto, J. Math. Anal. Appl. 200, No. 3, 680-686 (1996; Zbl 0855.34080)]. It is worth mentioning that in the case of first-order FDEs, the maximum principle (theorem 2.1) can be deduced from a more general result in [J. J. Nieto, Appl. Math. Lett. 15, No. 2, 173-179 (2002; Zbl 1014.34060)].
Reviewer: Eduardo Liz (Vigo)


34K10 Boundary value problems for functional-differential equations
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