### 博碩士論文 87241003 詳細資訊

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(On the positive solutions of nonlinear boundary value problems)

 ★ 非線性常微分方程式之邊界值問題的討論 ★ 有關於二階微分方程的非振動理論 ★ 函數微分方程正解存在性質

(*) u''(t)+f(t,u(t))=0, 0 u屬於B，其中B為適當的邊界條件。給予f(t,.)適當的條件，利用 Krasnoselskii 的固定點定理，我們將給出在幾種不同邊界值條件下的微分方程式多重正解的存在或非存在性。

u''(t)+f(t,u(t+s))=0, 0 來討論其解的存在性。更經由上述的延遲方程式的研究，

(**)u''(t)+f(t,u(g(t)))=0, 0 除了隱含方程式上的延遲性外，更可將一般的微分與差分方程做一個連結。

solutions of the following nonlinear boundary value problem of the form:
(*) u''(t)+f(t,u(t))=0, 0 Under the suitable condition f(t,.), by using Krasnoselskii''s fixed point theorem, we will give the existence and nonexistence of multiple positive solutions under several different boundary value conditions for the differential equations.
It follows from the boundary value problem (*), we can extend general ordinary diferential equation to the delay differential equations
u''(t)+f(t,u(t+s))=0, 0 and consider the existence of positive solutions.
Moreover, it follows from above delay differential equations, we find that the
differential equation on a measure chain defined on time scale of the form:
(**) u''(t)+f(t,u(g(t)))=0, 0 combine the difference and differential equations. So we deal with the existence of positive solutions of the problem (**).

★ 微分方程
★ 三正解
★ 三點邊界問題
★ 函數微分方程
★ 測度鏈
★ 存在性與非存在性
★ 二階系統

★ triple positive solutions
★ three-points boundary condition
★ functional differential equation
★ measure chain
★ second order systems
★ existence and nonexistence
★ nonlinear boundary value problems

On the positive solutions of nonlinear ordinary differential equations...1
Section 1.0.
Introduction.............................................................1
Section 1.1.
Triple positive solutions for boundary value problems....................8
Section 1.2.
On positive solutions for three-point boundary value problems ...........17
Section 1.3.
Multiple positive solutions for functional differential equations .......29
Chapter 2.
On the positive solutions of differential equations on a measure chain....42
Section 2.0.
Introduction .............................................................42
Section 2.1.
Existence and nonexistence of positive solutions for eigenvalue problems
on a measure chain ........................................................49
Section 2.2.
Existence of solutions for nonlinear second order systems on a measure
chain .....................................................................60
Reference.................................................................70

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