摘要
We study the existence of solutions to the second order three-point boundary value problem: where 0 <η< 1, α∈R, and f : [0, 1]×R×R→R, Ii: R×R→R, Ji : R×R→R(i=1,2,…k) are continuous. Our results is new and different from previous results. In particular, we obtain the Green function of the problem, which makes the problem simpler.
We study the existence of solutions to the second order three-point boundary value problem：{x″（t）＋f（t,x（t）,x′（t））=0,t≠ti,△x（ti）=Ii（x（ti）,x′（ti））,i=1,2,…,k,△x′（ti）=Ji（x（ti）,x′（t））,i=1,2,…,k,x（0）=0=x（1）-αx（η）,where 0〈η〈1,α∈R,and f：[0,1]×R×R→R,Ii：R×R→R,Ji：R×R→R（i=1,2,…,k）are continuous. Our results is new and different from previous results. In particular, we obtain the Green function of the problem, which makes the problem simpler.
基金
Supported by the National Natural Science Foundation of China(10371006)
关键词
二阶脉冲微分方程
三点边值问题
存在性
固定点
impulsive differential equation
boundary value problem
fixed points
cone
