一类奇异两点边值问题的正解

Positive Solutions of a Class of Singular Two-point Boundary Value Problems

本文研究了奇异二阶常微分方程边值问题其中α,β,γ,δ≥0,ρ=αγ+γβ+δα>0,并且允许h(t)在t=0和t=1处奇异,f(s)在s=0 处奇异．在关于相应线性算子第一特征值的条件下,得到正解的存在性结论．

The existence of positive solutions to singlar second-order boundary value problem {u″（t）＋h（t）f（u（t））=0, 0〈t〈1,;αu（0）-βu′（0）=0, γu（1）＋δu′（1）=1, is considered, under some conditions concerning the eigenvalues of relevant linear operator, where α,β,γ,δ≥0,ρ=αγ＋γβ＋δα〉0 and h（t） is allowed to be singular at t = 0 and t = 1, and f （s） is allowed to be singular at s = 0.