有關和米頓橢圓偏微分系統其解的唯一性與解結構及相關主題之探討;Uniqueness and Solution Structures of a Hamiltonian Elliptic System and Related Topics

Please use this identifier to cite or link to this item: http://ir.lib.ncu.edu.tw/handle/987654321/57029

Title:	有關和米頓橢圓偏微分系統其解的唯一性與解結構及相關主題之探討;Uniqueness and Solution Structures of a Hamiltonian Elliptic System and Related Topics
Authors:	陳建隆
Contributors:	中央大學數學系
Keywords:	數學類;唯一性;橢圓偏微分系統;非退化;線性化方程;Uniqueness;Elliptic System;Non-degeneracy;Linearized equations
Date:	2008-09-01
Issue Date:	2012-10-01 15:09:59 (UTC+8)
Publisher:	行政院國家科學委員會
Abstract:	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
Relation:	財團法人國家實驗研究院科技政策研究與資訊中心
Appears in Collections:	[Department of Mathematics] Research Project

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