一类二阶三点边值问题正解的存在性

Existence of positive solutions to a second order three-point boundary value problem

运用Leray Schauder不动点定理,讨论了边值问题 u″(t)+λa(t)f(u)=0, 0<t<1 u′(0)=0, αu(η)=u(1) 正解的存在性.其中η∈(0,1),α∈(0,1)是常数,允许a∈C[0,1]变号,f(0)>0,且λ充分小.

The existence of positive solutions of boundary value problemsu″(t)+λa(t)f(u)=0, 0<t<1u′(0)=0, αu(η)=u(1)is discussed by using Leray-Schauder fixed point theorem.Where η∈(0,1),0<α<1 are fixed constants,a∈C[0,1] may change sign, f(0)>0,and λ is sufficiently small.