无穷多点边值问题解的存在唯一性

Existence and Uniqueness of Solutions to ∞-Point Boundary Value Problem

考虑方程y″(t)=f(t,y(t),y′(t))+e(t)在边值条件y′(a)=0,y(b)=∑∞i=1aiy(ξi)下解的存在唯一性,其中f满足L2-Carath啨odory条件.在L2[a,b]中利用压缩映象原理得到解的存在唯一性结果.

Abstract： In this paper, the author discusses the existence and uniqueness of solutions to the equation y″（t）=f（t,y（t）,y′（t））＋e（t）,a≤t≤b, with ∞ - Point boundary value problem y′（a）=0,y（b）=∑i=1^∞aiy（ξi）.By contraction mapping principle, we get an optimum result in Banach space L^2（a, b） of the existence and uniqueness of solutions if f satisfies L^2 - Carathéodory conditions.