This paper systematically investigates a class of fourth-order differential equation with -Laplacian on infinite interval in Banach space. By means of the monotone iterative technique, we establish not only the existence of positive solutions but also iterative schemes under the suitable conditions. At last, we give an example to demonstrate the application of the main result.

中文翻译：

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带-拉普拉斯算子在无穷区间上的微分方程的迭代解

本文系统研究了一种类四阶微分方程的与-拉普拉斯上Banach空间中无穷区间。通过单调迭代技术，我们不仅建立了正解的存在性，而且建立了合适条件下的迭代方案。最后，我们通过一个例子来说明主要结果的应用。