g-(h,e)-混合单调算子及其应用

g-(h,e)-mixed monotone operator and applications

通过引入g-(h,e)-混合单调算子,利用锥理论和单调迭代法,对不动点的存在性和唯一性进行研究.针对Sturm-Liouville边值问题,应用主要结论研究其平凡解的存在性及唯一性.该文改进和推广了一些已有的结果,提出了一种研究非线性方程问题的新方法.

We study the existence and uniqueness of the fixed points by introducin g-(h,e)-mixed monotone operator and using the cone theory and the monotone iterative method. For the Sturm-Liouville boundary value problem, the existence and uniqueness of its ordinary solutions are studied by applying the main conclusions. In this paper, some existing results are improved and generalized, and a new method for studying nonlinear equation problems is proposed.