一类含参数非线性三阶两点边值问题正解的存在性

Existence of positive solutions for a class of nonlinear third-order two-point boundary value with parameter

本文借助于锥上的不动点定理,考虑如下一类非线性三阶两点点边值问题:{u?(t)+λa(t)f(u(t))=0,t∈(0,1),u(0)=u′(0)=u″(1)=0,解的存在性,其中λ>0,f:[0,+∞)→[0,+∞),连续a:(0,1)→[0,+∞),连续且满足0<∫_1~0(t-(1/2)(t^2))a(t)dt<+∞,允许a(t)在t=0或者t=1处奇异。

In this paper,we study the existence of positive solution to the following third-order two-point boundary value problems:ì{u'''(t)+λa(t)f(u(t))=0,t∈(0,1),u(0)=u′(0)=u″(1)=0,whereλis a positive parameter,f:[0,+∞)→[0,+∞)a:(0,1)→[0,+∞)are continuous,0<∫0 1(t-12 t2)a(t)dt<+∞and a(t)may be singular at t=0 or t=1,the proof of the main results is based on the fixed-point on cone.