一类奇异三阶两点边值问题正解的存在性

The Existence of Positive Solutions of a Class of Singular Third-order Two Point Boundary Value Problem

获得奇异三阶两点边值问题{u'''(t)+λa(t)f(u(t))=0,t∈(0,1),u(0)=u'(0)=u″(1)=0存在正解的最优条件,其中λ>0,f:[0,+∞)→[0,+∞)连续,a:(0,1)→[0,+∞)连续且满足0<∫10t(1-t)a(t)dt<+∞,允许a(t)在t=0或t=1处有奇性.主要结果的证明基于不动点指数理论.

In this paper, the optimal conditions for the existence of positive solutions are obtained for the singular third-order two point boundary value problem u″′（t）＋λa（t）f（u（t））=0,t∈（0,1）, u（0）=u＇（0）=u＇＇（1）=0 whereA is a positive parameter, λ〉0,f[0,＋∞）→[o,＋∞） anda：（0,1）→[o,∞）dt 0〈∫0^1（1-t）a（t）dt〈＋∞,maybe singular at t = 0 or t = 1. The proof of the main results is based on the fixed-point index theory.