一类非线性p-Laplacian差分方程边值问题的正解  

Positive Solution of a Class of Nonlinear p-Laplacian Difference Equations Boundary Value Problem

作　　者：杨丽[1] 

机构地区：[1]中北大学理学院,山西太原030051

出　　处：《中北大学学报（自然科学版）》2011年第5期540-544,共5页Journal of North University of China(Natural Science Edition)

摘　　要：通过采用构造凸泛函的方法,考察了一类非线性p-Laplacian型差分方程的正解存在性.借助相应的差分算子与适当的凸泛函,获得了此类边值问题至少存在一个正解的新的充分条件.所给出的条件仅涉及到非线性项在有界集上的性质,而未假定非线性满足超线性条件、次线性条件或上下解条件.通过一个具体的例子证明了结论的合理性.推广和改进了已有文献的部分结果.By using the method of constructing some convex functional,the existence of positive solution for p-Laplacian difference equations is considered.By mean of the corresponding difference operator and appropriate convex functional,the new sufficient conditions of at least a positive solution existence for this kind of boundary value problem are established.The given conditions only relate to the properties of the nonlinear term on bounded sets,without the assumptions of superlinearity,sublinearity or lower and upper solutions.The results are illustrated with an example,and extend and improve some known results.

关 键 词：凸泛函 差分方程 P-LAPLACIAN算子 

分 类 号：O175.8[理学—数学]