一类三阶两点边值问题正解的存在性和唯一性

Existence and Uniqueness of Positive Solution for the Third-Order Two-Point Boundary Value Problem

利用偏序集上的不动点定理证明了一个三阶两点边值问题:{u'''(t)+f(t,u(t))=0(t∈(0,1))u(0)=u'(0)=u″(1)=0正解的存在性和唯一性,并证明了该正解是严格单调递增的。

In this paper, we consider a third-order two-point boundary value problem：{u″′（t）＋f（t,u（t））=0（t∈（0,1））u（0）=u＇（0）=u″（1）=0 with the help of a fixed-point theorem in partially ordered sets, and obtained sufficient conditions for the ex- istence and uniqueness positive solution to the above boundary value problem. The result showed that this so- lution is strictly monotonic increasing.