二阶差分边值问题的正解

Positive Solutions of Second-order Difference Boundary Value Problems

本文研究了非线性项具有半正定和混合单调性的二阶差分边值问题正解的存在性.利用Krasnosel'skii不动点定理和锥拉伸与锥压缩不动点定理,讨论了二阶半正定非线性差分边值问题以及非线性项具有半正定和混合单调性的特征值问题正解的存在性,给出了这几类差分边值问题的正解存在性定理,改进和推广了具有正定非线性项的二阶差分边值问题的一些结果,并将所得结果应用于一个具体的二阶半正定非线性差分边值问题中.

The existence of positive solutions is studied for second-order difference boundary value problem with semipositone and mixedmonotonicity.By using Krasnosel＇skii＇s fixed point theorem and a fixed point theorem of cone expansion and compression in order type,the existence of positive solutions is studied for second-order difference boundary value problem with semipositone nonlinear term and the eigenvalue problem with semipositone and mixed-monotone nonlinear term,and some new existence theorems of positive solutions are achieved for these classes of systems,which improve the related results with positone nonlinear term.Our results are demonstrated by means of one example of second-order difference boundary value problem with semipositone nonlinear term.