臺灣博碩士論文加值系統

在本論文中，我們將討論非線性常微分方程式之邊界值問題。在第一、二章中，我們探討下列廣義的Laplacian 邊界值問題：
(g(u''))''=f(t,u(t),u''(t)), 0<t<1,
u 屬於 B
其中B是一個適當的邊界條件。考慮不同的函數g與f，我們給定適當的充分條件而得到正解的存在性與唯一性。
在第三、四章中，我們考慮下列四階微分方程式之邊界
值問題：
u''+rf(t,u(t))=0, 0<t<1,
u 屬於 B''
其中B’是一個適當的邊界條件。利用定點定理，給定函數 的條件，我們將討論解的存在性與多重性。

In this dissertation, we will study nonlinear boundary value problems for some ordinary differential equations. In chapters 1 and 2, we study the following generalized Laplacian boundary value problems :
(g(u''))''=f(t,u(t),u''(t)), 0<t<1.
We establish the solution existence and uniqueness for the problem under different conditions concerning f(t,u(t),u''(t)).
In chapters 3 and 4, we consider the following nonlinear fourth order boundary value problems :
u''+rf(t,u(t))=0, 0<t<1.
Consider different conditions concerning f(t,u(t)), we study the existence and multiplicity of solutions by using fixed point theorem.

Chapter 1. Existence and Uniqueness of Positive Solutions for Generalized Laplacian BVP''s with Sturm-Liouville Conditions ...........……….….(1)
Chapter 2. Existence of Positive Solutions for Generalized Laplacian Boundary
Value Problems ……………………………………………………...(26)
Chapter 3. Multiple Positive Solutions of Fourth Order Boundary Value
Problems ...........................................................................………......(39)
Chapter 4. Existence of Solutions for Singular Fourth Order Nonlinear
Boundary Value Problems ……………………………………….…(50)

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