一类二阶两点边值问题N个正解的存在性

Existence of N positive solutions for a class of second order two-point boundary value problem

运用单调迭代方法,研究二阶两点边值问题-u″(t)+αu(t)=f(t,u(t)),t∈(0,1)u(0)=u(1){=0多个正解的存在性.结果给出了此类问题N个对称正解存在性的充分条件,且得到了可将其精确解逼近到误差任意小的近似解迭代公式,其中N是任意自然数.

Apply to the monotone iterative techniques,the paper was concerned with the multiplicity of positive solutions for second order two-point boundary value problem-u″（t）＋αu（t）=f（t,u（t））,t∈（0,1）u（0）=u（1）=0.A sufficient condition was given about the existence of positive solutions in above problem,furthermore,we established iterative formula of approximate solutions with arbitrarily small error.