本論文共有六章︰第一章為簡介。第二章主要討論一維兩點邊界值拉普拉斯多重參數問題的正解全分枝性及確切正解個數。第三章主要研究一維兩點邊界值p-拉普拉斯多重參數問題，我們假設函數滿足(H1)-(H3)及((H4a)或(H4b))，在這些條件之下，我們利用時間映射(time map)的方法來研究此一問題，我們得到數種不同的分支曲線圖，而這些分支曲線不是單調曲線就是只有一個(朝右)轉折點之曲線。第四章主要研究一維兩點邊界值拉普拉斯多重參數問題，我們假設函數滿足(Ａ1)-(Ａ3)及((Ａ4a)或(Ａ4b))，在這些條件之下，我們得到更多不同的分支曲線圖，而這些分支曲線不是單調曲線就是只有一個(朝左)轉折點之曲線。在第五章裡，我們討論一維兩點邊界值p-拉普拉斯問題確切正解之個數，其中函數g是屬於weak Allee effect型式的函數。在最後一章裡，我們討論一維兩點邊界值p-拉普拉斯問題確切正解之個數，其中函數f是屬於有理形式的函數。

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