三阶二点边值问题三个正解的存在性

Existence of triple positive solutions for third order two-point boundary value problem

利用Leggett-Williams不动点理论,得到三阶二点边值问题:x′′′(t)+f(x(t))=0,0≤t≤1;x(0)=x′(0)=0,αx′(1)+βx′′(1)=0.至少存在3个正解的一个充分条件,其中α,β≥0且α+β>0.

The conditions on f（x） was found out which led to the existence of at least three positive solutions to the two-point boundary value problem x″（t） ＋ f（x（t）） = 0, 0 ≤ t ≤1; x（0）= x′（0）=0, αx′（1）＋βx″（1）=0. Where α, β≥0 and α＋β〉0.