摘要
考虑以下三阶三点边值问题:{u'''(t)+f(t,u(t))=0,t∈(0,1),u'(0)=u″(0)=0,u(1)=αu(η),其中0<η<1,0<α<1.通过建立相关线性边值问题的格林函数得到解的形式,运用不动点指数理论建立了上述边值问题的正解的存在性准则.
We concerned with the following third-order three-point boundary value problem {u″（t）＋f（t,u（t））=0,t∈（0,1）,u′（0）=u″（0）=0,u（1）=αu（η） where0〈η〈1 ,and 0〈α〈 1 . By establishing Green function for the associated linear boundary value problem, thesolution for the above boundary value problem is obtained. Then the existence criterion of positive solutions for theabove boundary value problem is obtained by using fixed point index theorem.
出处
《山东师范大学学报（自然科学版）》
CAS
2017年第2期30-34,共5页
Journal of Shandong Normal University(Natural Science)
关键词
三阶三点边值问题
正解
存在性
锥
格林函数
不动点指数理论
third-order three-point boundary value problem
Green function
fixed point index theorempositive solution
existence
cone
