二阶非线性边值问题解的存在唯一性

Existence and Uniqueness of Solutions for Point Boundary Value Problem

考虑带边值条件y(a)=0,y(b)=sum from i=1 to ∞ (aiy(ζi))的二阶非线性微分方程y″(t)=f(t,y(t),y′(t))+e(t),其中f满足L2-Carathe'odory条件.运用压缩映象原理在L2(a,b)空间中研究问题解的存在唯一性结果.

In this paper, the author discusses second order nonlinear differential equation as follows.y（a） = 0,y（b） =∞∑i=1 aiy（ξi） with boundary value problem y″（t）=f（t,y（t）,y′（t））＋e（t） ,where L^2 - satisfies Caratheodory conditions. Contraction mapping principle is employed to study the existence and uniqueness of this problem.