非线性二阶微分方程两点边值问题正解的存在性

THE EXISTENCE OF POSITIVE SOLUTIONS TO NONLINEAR SECOND ORDER DIFFERENTIAL EQUATION WITH TWO POINT BOUNDARY VALUE PROBLEM

本文通过构造Ｇｒｅｅｎ函数，借助锥不动点定理证明了非线性二阶微分方程两点边值问题ｕ＂十ｍ~２ｕ＋ｆ（ｔ，ｕ）＝０，ｕ（０）＝ｕ（１）＝０，正解的存在性．

The existence of positive solutions to second-order two point BVPs u'+m^2 +f(t,u)=0, u (0) =u(1) =0, is proved by a simple application of a Fixed Point Theorem in cones.