一类三阶三点边值问题正解的存在性

考虑一类三阶三点边值问题u(t)+a(t)f(u(t))=0,t∈(0,1),u(0)=u’(0)=0,u’(1)-αu’(η)=λ, 其中,0<η<1,0<α<1/η,λ>0,f满足超线性或者次线性条件,利用锥上的不动点定理,得到上述边值问题解的存在性结果.结果表明:文中方法进一步改进和推广了吴红萍的结果.

Existence of Positive Solution for Third-Order Three-Point Boundary Value Problems

We study the existence of positive solution to the following third-order three-point boundary value problems u(t)+a(t)f(u(t))=0, t∈(0,1), u(0)=u’(0)=0, u’(1)-αu’(η)=λ, where 0<η<1, 0<α<1/η, λ>0. By using fixed point theorem in cones, we obtain the existence of the positive solution if f is either superlinear or sublinear. Our results extend and improve some results made by Wu Hongping.