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

Positive Solutions for(n-1,1) m-Point Boundary Value Problems With Dependence on the First Order Derivative

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f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.

Using the extension of Krasnoselskii＇ s fixed point theorem in a cone, 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 was proved. The associated Green＇s function for the nth order mpoint boundary value problem was given, and growth conditions were imposed on nonlinear term f which ensure existence of at least one positive solutions. A simple example was presented to illustrate applications of the obtained results.