Unique Results for a New FourthOrder Boundary Value Problem 
Received:January 17, 2018 Revised:July 17, 2018 
Key Words:
fourthorder boundary value problem unique solution $\varphi$$(h,e)$concave operator existence and uniqueness

Fund Project:Supported by the Shanxi Scholarship Council of China (Grant No.2016009) and the Natural Science Foundation of Shanxi Province (Grant No.201701D121004). 

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Abstract: 
In this paper, we investigate the existence and uniqueness of solutions for a new fourthorder differential equation boundary value problem: $$\left\{ \begin{array}{l} u^{(4)}(t)=f(t,u(t))b,\ 0< t<1,\\ u(0)=u'(0)= u'(1)= u^{(3)}(1)=0, \ \end{array}\right. $$ where $f\in C([0,1]\times(\infty,+\infty),(\infty,+\infty)),\ b\geq 0$ is a constant. The novelty of this paper is that the boundary value problem is a new type and the method is a new fixed point theorem of $\varphi$$(h,e)$concave operators. 
Citation: 
DOI:10.3770/j.issn:20952651.2018.05.006 
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