具有各阶导数的高阶边值问题的正解存在性

Positive solutions for high-order boundary value problems with dependence on all derivatives

利用锥上的一个不动点定理,给出了非线性项中含有各阶导数的高阶边值问题正解存在的充分条件,为此,首先给出相应边值问题的Green函数,然后赋予非线性项一定的增长条件。

By using a fixed point theorem in a cone, the sufficient conditions of the existence of positive solution for high-order BVPs with all derivatives are provided. Firstly the associated Green＇s function is given. Then the growth conditions are imposed on the nonlinear term which ensure the existence of positive solution to the problems.