一类奇异二阶边值问题正解存在的充分必要条件  

A NECESSARV AND SUFFICIENT CONDITION FOR THE EXISTENCE OF POSITIVE SOLUTIONS TO A CLASS OF SINGULAR SECOND-ORDER BOUNDARV VALUE PROBLEMS

作　　者：郝兆才[1] 毛安民[1] 

机构地区：[1]曲阜师范大学数学与计算机科学系,曲阜273165

出　　处：《系统科学与数学》2001年第1期93-100,共8页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金;山东省自然科学基金

摘　　要：本文研究了一类奇异二阶边值问题ｕ＇＇＋ａ（ｔ）ｆ（ｕ）＋ｂ（ｔ）ｇ（ｕ）＝０，αｕ（０）－βｕ＇（０）＝０，γｕ（１）＋δｕ＇（１）＝０的Ｃ１［０，１］的正解．在ｆ和ｇ同为超（次）线性和一个为超线性、一个为次线性的情形下均得到了 Ｃ１［０，１］正解存在的充分必要条件，推广和包含了一些已知结果．This paper studies the C1[0, 1] positive solutions of a class of second-order boundary value problems u' + a(t)f(u) + b(t)g(u) = 0, u(0) - A necessary and sufficient condition for the existence of C1 [0, 1] positive solutions is obtained under the condition that f and g are all superlinear (sublinear), or one is superlinear, the other is sublinear, which generalizes and includes some known results.

关 键 词：奇异边值问题 锥 正解 充要条件 存在性 次线性 超线性 

分 类 号：O175.8[理学—数学]