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

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.