摘要
考虑方程ｙ″＋ｆ（ｔ，ｙ，ｙ′）＝０在边值条件ｙ（ａ）＝Ａ，ｙ（ｂ）＝Ｂ下解的存在唯一性．要求ｆ满足Ｌ２－Ｃａｒａｔｈｅｏｄｏｒｙ条件，在Ｌ２空间中利用压缩映象原理得到解唯一存在的最优结果．
In the paper we study the existence and uniqueness of solutions for the equation y″+f(t,y,y′)=0 with the boundary conditions u(a)=A, u(b)=B. By contraction mapping principle we get an optimum result in Banach space L 2(a,b) of the existence and uniqneness of solutions if f satisfies L 2 Caratheodory conditions.
出处
《纯粹数学与应用数学》
CSCD
1998年第2期61-64,共4页
Pure and Applied Mathematics
关键词
非线性
边值问题
压缩映象
解
存在性
唯一性
nonlinear boundary value problem
contraction mapping principle
optimum result
