退化的p拉普拉斯方程式在最近被廣泛的研究，p拉普拉斯算子與幾個領域有關，如非牛頓流體力學、非線性過濾相關的理論等。它也可被視為廣為人知拉普拉斯方程式的推廣，當p退化成2時。在本篇論文中，我們研究一個相互連結的一維微分方程系統。附註說明，在此考慮的相互連結系統是比單一方程在數學分析處理上複雜許多。本文嘗試去研究會改變符號的解其存在性。在此我們介紹一個有效率的方法，修正後的Prufer代換，去研究此問題的相關性質。

The degenerate p-Laplacian equations have been extensively studied recently. It is relted to several fields, the non-Newtonian fluids, the nonlinear filtration theory, and etc. It also can be treated as a generalization of the Laplacian operator when p=2. In this paper, we study a coupled system of one-dimensional p-Laplacian equations. Note that the problem we concerned is more complicated to uncoupled systems. We intend to study the existence of sign-changing solutions of this problem. Here we introduce an efficient method, modified Prufer substitutions, to study some related properties of this problem.