Banach空间中一类四阶两点边值问题的正解的存在性(英文)

The Existence of Positive Solutions for a Fourth-order Two-point Boundary Value Problem in Banach Spaces

利用Darbo不动点定理,研究了Banach空间中一类四阶两点边值问题x(4)(t)=f(t,u(t),u″(t)),t∈I,x(0)=x′(1)=x″(0)=x(1)=θ,正解的存在性.并给出了例子用来阐明该文的结果.

In this paper,by using the Darbo-fixed-point theorem,the existence of positive solution for the fourth-order two-point boundary value problem x（4）（t）=f（t,u（t）,u″（t））,t∈I, x（0）=x′（1）=x″（0）=x（1）=θin Banach spaceE is studied,whereI=[0,1],f∈C[I×E×E,E].θis the zero element ofE.As an applica-tion,one example to demonstrate our results is given.