P-拉普拉斯狄利克雷問題分枝曲線之完整分類

這篇碩士論文中，我們研究的問題是「p拉普拉斯狄利克雷問題」正解個數的存在性。
第一節『序言』：我們先介紹什麼是「p拉普拉斯狄利克雷問題」，並且說明它在實際生活上可以運用到哪些地方。接著，再回顧一些學者所做過相類似的問題。在這篇論文裡，我們採用所謂「時間函數」的方式來檢測解的個數，在序言中，我們先介紹何謂「時間函數」，並且介紹「時間函數」一些已知的性質。
第二節『主要結果』：因為証明需要，在這裡先介紹一些特殊函數：「gamma function」、「psi function」、「hypergeometric function」以及「Euler’s constant」。定理2.1.把時間函數用特殊函數表現出來，藉此，我們可以比較清楚地描述時間函數。定理2.2.則把時間函數的所有特徵描述出來，從這個定理，我們可以清楚地知道任給一個p大於1、q大於0，其時間函數的圖形。接著，在推論2.3.中我們就可以清楚地指出這個問題正解的個數。在定理2.4.中，對於固定的p大於1，我們比較當q不同時其時間函數的大小關係。
第三節『主要定理的証明』：我們利用前面介紹過特殊函數的一些性質以及加入我們的想法，把上述定理給完整證明。
第四節『參考書目』：介紹這篇論文所引用到的文獻。

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