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

47H10Fixed point theorems for nonlinear operators on topological linear spaces
34B15Nonlinear boundary value problems for ODE
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[5]Ran, A.C.M. and Reurings, M.C.B.: A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Am. Math. Soc. 132 (2004), 1435–1443. · Zbl 1060.47056 · doi:10.1090/S0002-9939-03-07220-4
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