在此計畫中, 我們將討論下數橢圓偏微分系統其中 利用變分法的方法, 考慮下述泛函, 他們證明了: 對任何上述 (1.1)-(1.2) 方程的解 (u,v), 均是對全空間的某一特定點是軸對稱的, 而且其在無窮遠的行為亦均是指數遞減至零. 在此計畫裡, 我們考慮下列較一般的系統我們欲利用:我們剛在 Chern-Simons-Higgs 模型中, 利用其拓樸解所對應的非退化特性及變型論正法(Ref: Jann-Long Chern, Z.-Y. Chen and Chang-Shou Lin, Uniqueness of Topological Solutions and the Structure of Solutions for the Chern-Simons Equations with Two Higgs Particles, Preprint), 來嘗試證明此種解的唯一性, 進而了解其所有解的結構性. ; In this project, we will study following elliptic system The main purpose of this project is to prove the uniqueness problem and complete the solutions structures of equation (2.3). We will try to study this researches by applying the deformation arguments and methods in the non-degeneracy property of linearized equation at topological solution for Chern-Simons-Higgs Model (See Jann-Long Chern, Z.-Y. Chen and Chang-Shou Lin, Preprint). ; 研究期間 9708 ~ 9807
