一类四阶三点边值问题的正解的存在性

The existence of positive solution for a four-order three-point boundary value problem

研究u(4)(t)-F(t,u(t))=0在边值条件u(0)=u′(0)=u″(η)=u (1)=0,1 3≤η<1下正解的存在问题,主要工具和方法是利用Krasnoselskli锥不动点定理,从而证明了方程至少存在一个正解.

In this paper, we study the BVPu~ (4)(t)-F(t, u(t))=0(0≤t≤1)u(0)=u′(0)=u″(η)=u(1)=0(1/3≤η<1)(P)The main tool is Krasnoselskli fixed-piont theorem on cone, and we obtained BVP (P) has at least one positive solution.