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**Fixed point theorems in partially ordered metric spaces and applications.**
*(English)*
Zbl 1106.47047

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.

Reviewer: Zhang Xian (Xiamen)

### MSC:

47H10 | Fixed-point theorems |

34B15 | Nonlinear boundary value problems for ordinary differential equations |

54H25 | Fixed-point and coincidence theorems (topological aspects) |

54F05 | Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces |

### Keywords:

coupled fixed point; partially ordered set; coupled upper, lower solution; periodic boundary value problem
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\textit{T. G. Bhaskar} and \textit{V. Lakshmikantham}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 65, No. 7, 1379--1393 (2006; Zbl 1106.47047)

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### References:

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