本篇論文，旨在探討準線性橢圓邊界值問題之解路徑的問題。我們使用五點分割的中央有限差分法、割線預測法、牛頓迭代法、隱函數定理、虛擬弧長延拓法，找出我們的準線性橢圓模型在有限邊界內之解路徑，其中包括找出其轉彎點與分歧點，並對其解路徑之分歧與延拓加以分析，探討準線性橢圓問題之解路徑的變化。

In this paper , we investigate the solution paths of a quasilinear elliptic equation with boundary values . We use the central finite difference method , secant predictor , newton’s iterative method , implicit function theorem ,
pseudo-arclength continuation method to find the solution paths of the model .
Furthermore , we will locate the turning points and bifurcation points of the solution paths of the model . We also investigate of the solution paths of the quasilinear elliptic model .

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