摘要
利用压缩映射原理讨论了边值问题y(4)(t)=f(t,y,y′,y,″y′″),y(a)=y(b)=0,y″(a)=y″(b)=0解的存在唯一性问题,得出了当f满足Lipschitz条件时边值问题解的存在唯一性定理,并证明了当f为半线性f(t,y)时结论是最优的.同时给出了一个改进的Picard迭代误差公式,此公式保证了端点处误差为零.
Abstract： Used contraction mappings fixed point theorem, this paper discussed the existence and uniqueness of boundary value problems as followes：y^（4）（t）=f（t,y,y＇y＇＇,y＇＇）,y（a）=y（b）=0,y＇＇（a）=y＇＇（b）=0.We get the existence and uniqueness theorem of BVP when f the best when f was semilinear. At the same time we get an satisfy Lipschitz condition, and proved that the result was improved Picard iteration error formula which ensured the error was zero at two points.
出处
《大学数学》
2009年第3期110-117,共8页
College Mathematics
基金
教育部新世纪人才支持计划项目(NCET-07-0449)
关键词
存在性
唯一性
边值问题
GREEN函数
压缩映射原理
existence
uniqueness
boundary value problem
Green function
contraction mappings fixed point theorem
