非線性常微分方程式之邊界值問題的討論; Nonlinear Boundary Value Problems for Some Ordinary Differential Equations

Please use this identifier to cite or link to this item: http://ir.lib.ncu.edu.tw/handle/987654321/7766

Title:	非線性常微分方程式之邊界值問題的討論;Nonlinear Boundary Value Problems for Some Ordinary Differential Equations
Authors:	李中芬;Chung-Fen Lee
Contributors:	數學研究所
Keywords:	非線性常微分方程式;邊界值問題;Laplacian 邊界值問題;定點定理;存在性與唯一性;ordinary differential equations;nonlinear boundary value problems;existence and uniqueness;fixed point theorem;Laplacian boundary value problems
Date:	2002-05-17
Issue Date:	2009-09-22 11:04:51 (UTC+8)
Publisher:	國立中央大學圖書館
Abstract:	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.
Appears in Collections:	[Graduate Institute of Mathematics] Electronic Thesis & Dissertation

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