一类非线性二阶三点边值问题的正解(英文)

Positive Solutions to a Class of Nonlinear Second-Order Three-Point Boundary Value Problems

考察了二阶三点边值问题u"(t)+f(t,u(t))=0,0<t<1;αu(0)=βu'(0),ku(η)=u(1)的正解存在性与多解性,其中允许f(t,u)在t=0,t=1处奇异.利用锥上的Krasnosel’skii不动点定理获得了几个局部存在定理.

The existence and multiplicity of positive solutions are considered for the second-order threepoint boundary value problem u＂（t） ＋ f（t,u（t）） = 0, 0 〈 t 〈 1; αu（0） = βu＇（0）, ku（η） = u（1）, where f（t,u） is allowed to be singular at t = 0, t = 1. Several local existence theorems are obtained by applying the Krasnosel＇skii fixed point theorem on cone.