In this paper, we present a new fixed point theorem for the sum of two mixed monotone operators of Meir–Keeler type on ordered Banach spaces through projective metric, which extends the existing corresponding results. As applications, we utilize the results obtained in this paper to study the existence and uniqueness of positive solutions for nonlinear singular fourth-order elastic beam equations with nonlinear boundary conditions.

中文翻译：

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Meir–Keeler型两个混合单调算子之和的新不动点定理及其在非线性弹性梁方程中的应用

在本文中，我们通过投影度量为有序Banach空间上Meir–Keeler类型的两个混合单调算子的和提出了一个新的不动点定理，扩展了现有的相应结果。作为应用，我们利用本文中获得的结果来研究具有非线性边界条件的非线性奇异四阶弹性梁方程正解的存在性和唯一性。