Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations. (English) Zbl 1095.47013

Nieto, Juan J.; Rodríguez-López, Rosana

Order 22, No. 3, 223-239 (2005).

The main results of this interesting paper are existence and uniqueness theorems for a periodic boundary value problem. The approach is based on some fixed point theorems on a partially ordered set. The fixed point results are in close connections with some results given by A. C. M. Ran and M. C. B. Reurings [Proc. Am. Math. Soc. 132, No. 5, 1435–1443 (2004; Zbl 1060.47056)] and by A. Petruşel and I. A. Rus [ibid. 134, No. 2, 411–418 (2006; Zbl 1086.47026)].

Reviewer: Adrian Petruşel (Cluj-Napoca)

MSC:

47H10	Fixed-point theorems
34B15	Nonlinear boundary value problems for ordinary differential equations

Keywords:

fixed point; differential equation; lower solution; upper solution; contraction mapping

Citations:

Zbl 1060.47056; Zbl 1086.47026

References:

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