在本篇文章中，我們將探討橢圓方程和橢圓系統中解的存在性、唯一性及結構性等問題。首先，在橢圓方程中，我們將利用特徵方程來了解某些奇異解的存在性和唯一性， 接者再使用 Pohozeaev function 和 Energy function 來了解其他所有解的存在性和結構性。 然而在橢圓系統中， 我們將透過線性化方程來學解的結構性，進一步結合隱函數定理來證明某些解的唯一性。 In this article, we consider problems involving the existence, uniqueness, and structure of solutions for (single) elliptic equations and (coupled) elliptic systems. To deal with the elliptic equations, we first employ the characteristic equations to realize the existence and uniqueness of certain singular solutions. Then, specific auxiliary functions, Pohozaev functions and energy functions, will be introduced to conduct the uniqueness for solutions of other types and clarify the complete structure of solutions. On the other hand, for the elliptic systems, we analyze the structure of solutions by means of the corresponding linearized equations. Furthermore, combining the Implicit Function Theorem, the consequences related to the uniqueness of some solutions will be offered as well.
