依赖于一阶导数的(n-1,1)共轭m点边值问题正解的存在性

利用锥上的Krasnoselskii's不动点定理的推广定理,讨论了一类边值问题,给出了相应依赖于一阶导数的非线性n阶m点边值问题至少一个正解的存在性.对于n阶m点边值问题,给出了相应的Green 函数.证明了在非线性项厂满足一定的增长条件下至少存在1个正解.并且给出了一个例子来说明所获得的结果.     

Positive solutions to （n-1,1） m-point boundary value problems with dependence on the first order derivative

Using the extension of Krasnoselskii＇s fixed point theorem in a cone, we prove the existence of at least one positive solution to the nonlinear nth order m-point boundary value problem with dependence on the first order derivative. The associated Green＇s function for the nth order m-point boundary value problem is given, and growth conditions are imposed on the nonlinear term f which ensures the existence of at least one positive solution. A simple example is presented to illustrate applications of the obtained results.