In this paper, we employ partial order method, cone theory, and the techniques of measure of weak noncompactness to prove several new theorems on the existence and the uniqueness of fixed points or coupled fixed points for operators satisfying some monotonicity assumptions. Our conclusions generalize and improve several well-known results. As an application, we investigate the existence of a unique solution for a class nonlinear second-order ordinary differential equations. We also discuss the existence of a unique solution for a system of integral equations.

中文翻译：

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部分有序Banach空间中单调算子不动点的存在性和唯一性

在本文中，我们采用偏序方法，锥理论和弱非紧致性的度量技术，证明了满足满足单调性假设的算子的不动点或耦合不动点的存在性和唯一性的几个新定理。我们的结论概括并改进了一些著名的结果。作为一种应用，我们研究了一类非线性二阶常微分方程唯一解的存在。我们还讨论了积分方程组唯一解的存在。