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Zbl 1106.47047
Bhaskar, T. Gnana; Lakshmikantham, V.
Fixed point theorems in partially ordered metric spaces and applications. (English)
[J] Nonlinear Anal., Theory Methods Appl. 65, No. 7, A, 1379-1393 (2006). ISSN 0362-546X

This paper gives some coupled fixed point theorems for a monotone mapping in a metric space endowed with a partial order, using a weak contractivity type assumption. Besides including several recent developments, the theorems can be used to investigate a class of problems. As an application, the existence and uniqueness of solutions for a periodic boundary value problem are discussed.
[Zhang Xian (Xiamen)]

MSC 2000:: *47H10 Fixed point theorems for nonlinear operators on topol.linear spaces
34B15 Nonlinear boundary value problems of ODE
54H25 Fixed-point theorems in topological spaces
54F05 Ordered topological spaces

Keywords: coupled fixed point; partially ordered set; coupled upper, lower solution; periodic boundary value problem

Cited in: Zbl 1255.54027 Zbl 1247.54048 Zbl 1236.47056 Zbl 1235.47094 Zbl 1235.54041 Zbl 1230.54047 Zbl 1225.54029 Zbl 1225.54014 Zbl 1218.54040 Zbl 1215.54020 Zbl 1202.54036 Zbl 1229.54051 Zbl 1205.54044 Zbl 1204.47067 Zbl 1198.65097 Zbl 1176.54032

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