利用一个新的锥不动点定理和非局部边值问题的Green函数的性质,研究了一类含有一阶导数的非局部四阶边值问题:{u(4)(t)+Au″(t)=λf(t,u(t),u′(t)),00,0
In this paper, a new fixed point theorem and the properties of Green function are used for the nonlocal boundary val- ue problems. The existence of at least one positive solution to the nonlocal fourth-order boundary value problem with the first order derivative is considered, where f is a nonnegative continuous function and λ〉0,0〈A〈π2 ,p,q∈ L[0,1],p(s)≥0,q(s)≥0. Finally, a simple example is presented to illustrate the correctness of the obtained results.