具一般非線性函數 Dirichlet-Neumann 邊界問題之分枝曲線分類與演化及其應用

Classification and evolution of bifurcation curves for a Dirichlet-Neumann boundary value problem with general nonlinearity and its application

郭達昌(Kuo, Da Chang)

指導教授 ： 王信華

國立清華大學/理學院/數學系/碩士(2016年)

摘要

我們研究在Dirichlet-Neumann邊界條件下的正解分枝曲線的分類與演化，u''(x)+λf(u)=0, 00，是分枝參數；而c>0，是演化參數。我們主要要證明函數f在適當的假設下，我們可以找到一個c₁>0，使得在(λ,‖u‖∞)平面上，我們有以下兩個性質。
(1)當0

關鍵字

Dirichlet-Neumann邊界值問題 ； 分枝曲線的演化 ； 分枝曲線的分類 ； 分枝曲線 ； 時間圖

並列摘要

We study the classification and evolution of bifurcation curves of positive solutions for the Dirichlet-Neumann boundary value problem u''(x)+λf(u)=0, 00 is a bifurcation parameter and c>0 is an evolution parameter. We mainly prove that, under some suitable assumptions on f, there exists c₁>0, such that, on the (λ,‖u‖∞)-plane, (i) when 0

並列關鍵字

Dirichlet-Neumann boundary value problem ； evolution of bifurcation curve ； classification of bifurcation curve ； bifurcation curve ； time map ； general nonlinearity

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