在本論文中,我們討論下列時滯邊界值問題egin{eqnarray*}(BVP)left{begin{array}{l}y'(t)+q(t)f(t,y(sigma(t)))=0, tin(0,1)/{ au},
y(t)=xi(t), tin[- au_{0},0],
y(1)=0,end{array}
right.
end{eqnarray*},其中函數f和g滿足特定條件$sigma(t)leq t$是一個非線性實值連續函數.我們利用固定點定理和漸近逼近兩種方法,給出上述邊界值問題正解存在的充分條件.主要的貢獻在放將時滯項由線性函數推廣到非線性函數,對於Agarwal及O'Regan和Jiang及Xu在線性時滯項已知的結果,我們可以得到更一般化和完備化的結果.

In this thesis, we consider the following delay boundary value problem
egin{eqnarray*}(BVP)left{begin{array}{l}y'(t)+q(t)f(t,y(sigma(t)))=0, tin(0,1)/{ au},
y(t)=xi(t), tin[- au_{0},0],
y(1)=0,end{array}
right.
end{eqnarray*}, where the functions f and q satisfy certain conditions; $sigma(t)leq t$ is a nonlinear real valued
continuous function.
We use two different methods to establish some existence criteria for the solution of problem
(BVP). We generalize the delay term to a nonlinear function and obtain more general and
supplementary results for the known ones about linear delay term due to Agarwal and O’Regan
[1] and Jiang and Xu [5].

1 Introduction 3
2 Preliminaries 5
3 Existence Results - Fixed Point Method 7
4 Existence Results - Limiting Method 13
5 Application 20

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