一类高阶奇异边值问题的正解  

Positive Solutions of Singular Boundary Value Problems of a Class of Higher Order Differential Equations

作　　者：邓义华[1] 

机构地区：[1]衡阳师范学院数学系,湖南衡阳421008

出　　处：《江西师范大学学报（自然科学版）》2007年第4期419-423,共5页Journal of Jiangxi Normal University(Natural Science Edition)

基　　金：湖南省自然科学基金资助项目(06JJ5001);衡阳师范学院青年课题(2005A12)

摘　　要：利用格林函数将一类高阶奇异边值问题转化为与之等价的算子方程,然后构造合适的辅助函数,利用极大值原理和上下解方法,得到了这类边值问题存在C2n-1[0,1]∩C2n(0,1)正解的充分必要条件.The transformation from singular boundary value problems of a class of higher order differential equations to its equivalent operator equations by using of Green function is utilized. By constructing a proper assistant function and using the maximal theorem as well as lower and upper solutions, a necessary and sufficient condition for the existence of positive solution is obtained.

关 键 词：正解 奇异边值问题 存在性 极大值原理 

分 类 号：O175.8[理学—数学]