本論文主要探討在有界域上的奇異擾動橢圓方程，其中我們考慮Robin多點邊界條件(涉及到未知解在內點的行為)。我們建立一個標準的橢圓方程以及對應的映射與原方程做連結，將問題轉化為尋找該映射的固定點的問題。我們利用固定點理論得到該映射存在唯一固定點的一個充分條件，從而證明了原方程的解的存在性和唯一性。此外，本文還提供了一個例子，展示了方程可能有多個解或無解的情況。

This thesis primarily investigates singularly perturbed elliptic equations in bounded domains, where we consider Robin multi-point boundary conditions (involving the behavior of the unknown solution at interior points). We establish a standard elliptic equation and a corresponding mapping linked to the original equation, transforming the problem into finding the fixed point of this mapping. By utilizing fixed point theory, we obtain a sufficient condition for the existence of a unique fixed point of this mapping, thereby proving the existence and uniqueness of solutions for the original equation. Additionally, this thesis provides an example demonstrating that the equation may have multiple solutions or no solution at all.

Table of Contents
摘要 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii
誌謝 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
3 Proof of Theorem 1.1 . . . . . . . . . . . . . . . . . . . . . . . . 16
A Appendix A: Proof of Example 1.1 . . . . . . . . . . . . . . . 23
B Appendix B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

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