本論文共有五章︰第一章為簡介。第二章主要討論一維規定的平均曲率問題的正解個數。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枝曲線圖。第三章主要藉由數值模擬來研究此一問題，我們得到數種不同的分枝曲線圖，發現到有演化的現象。第四章證明需要用到的引理。第五章是理論證明。

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