二階非線性斯圖謨-劉維爾方程兩點(diǎn)邊值問題的研究.pdf

1、安慶師范學(xué)院碩士學(xué)位論文二階非線性斯圖謨-劉維爾方程兩點(diǎn)邊值問題的研究姓名：陳健申請(qǐng)學(xué)位級(jí)別：碩士專業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)教師：王其申2011-06-082Abstract Abstract The main topic of this dissertation is research into the boundary value problem of the following equation： ( ) ( ) ( ) ( ( ))

2、 0 0 1(0) 0, (1) 0p x u x f u x xu u? ′ ′ ? + = < < ? = = ? ?(1) where ( ) p x or ( ) p x ′is a piecewise linear function. The first chapter is introduction which summarizes the status quo of the research. The c

3、oncept of cone and cone expansion and compression fixed point theorem which is prior knowledge of the prove，is introduced in the second chapter. The third chapter is research into the Green Functions of Homogeneous equa

4、tion which corresponding the equation (1) when p(x) as the following equation: 121 0 2 ( ) 1 1 2p x p xp x? < ≤ ? ? = ? ? ≤ < ? ?, and use the cone expansion and compression fixed point theorem probe into

5、 the existence of solutions of the boundary value problem (1). Then，In the fourth chapter the content of the third chapter is extended to the situation that 120 ( ) 1p x c p x p c x< ≤ ? = ? ≤ < ? . The fifth chap