Symmetric Positive Solutions of Nonlinear Singular Second-order Three-point Boundary Value Problem

In this paper, the second-order three-point boundary value problem u(t) + λa(t)f(t, u(t)) = 0, 0 < t < 1,u(t) = u(1- t), u(0)- u(1) = u(12)is studied, where λ is a positive parameter, under various assumption on a and f, we establish intervals of the parameter λ, which yield the existence of positive solution, our proof based on Krasnosel'skii fixed-point theorem in cone.{u"(t)+λa(t)f(t,u(t))=0,0<t<1,u(t)=u(1-t),u′(0)-u′(1)=u(1/2)is studied,where A is a positive parameter,under various assumption on a and f,we establish intervals of the parameter A,which yield the existence of positive solution,our proof based on Krasnosel'skii fixed-point theorem in cone.

In this paper, the second-order three-point boundary value problem u（t） ＋ λa（t）f（t, u（t）） = 0, 0 〈 t 〈 1,u（t） = u（1- t）, u（0）- u（1） = u（12）is studied, where λ is a positive parameter, under various assumption on a and f, we establish intervals of the parameter λ, which yield the existence of positive solution, our proof based on Krasnosel＇skii fixed-point theorem in cone.{u＂（t）＋λa（t）f（t,u（t））=0,0