一类2n阶奇异边值问题的正解(英文)  

On the Existence of Positive Solutions for 2n-order Singular Boundary Value Problem

作　　者：刘树宽[1] 杜新生[2] 

机构地区：[1]济宁学院数学系,273100 [2]曲阜师范大学数学科学学院,山东省曲阜市273165

出　　处：《曲阜师范大学学报（自然科学版）》2007年第2期7-12,共6页Journal of Qufu Normal University(Natural Science)

基　　金：Research supported by the National Natural Science Foundation of China(10471075);the Natural Science Foundation of Shandong Province(Y2006A04);the Doctoral Program Foundation of Education Ministry of China(20050446001).

摘　　要：通过利用单调迭代技巧,上下解方法及最大值原理讨论了一类2n阶奇异边值问题,得到了C(2n-1)[0,1]正解存在的充分必要条件及C(2n-2)[0,1]正解存在的充分条件.A necessary and sufficient condition for the existence of C^（2n-1）[0,1] positive solutions to the singular boundary has been obtained by using the monotone iterative techniques. By constructing lower and upper solutions and with the maximal theorem, a sufficient condition for the existence of C^（2n-2）[0,1] positive solutions is also given.

关 键 词：正解 高阶微分方程 上下解 最大值原理 

分 类 号：O175.8[理学—数学]