This paper provides a class of upper and lower solution definitions for second-order coupled systems by transforming the fourth-order differential equation into a second-order differential system. Then, by constructing a homotopy parameter and utilizing the maximum principle, we propose an upper and lower solutions method for studying a class of second-order coupled systems with Dirichlet boundary conditions and obtain an existence result.

中文翻译：

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一类二阶耦合系统的上下解法

本文通过将四阶微分方程转化为二阶微分系统，给出了一类二阶耦合系统的上、下解定义。然后，通过构造同伦参数并利用极大值原理，提出了研究一类具有狄利克雷边界条件的二阶耦合系统的上下解方法，并得到了存在性结果。