摘要
本文通过某种非线性变换,将非线性两点边值问题-v″+v'2/v=1,x∈(0,1),v(0)=v(1)=0转化为blow-up边值问题u″=eu,lim x→0+u(x)=lim x→1-u(x)=+∞,进而得到该两点边值问题存在非负解并给出该解的解析式。这也为我们求解常微分方程提供了一种新方法。
By a kind of nonlinear transform, the nonlinear two - point boundary value problem -v＇＇＋v＇2/v=1,x∈（0,1）,v（0）=v（1）=0 is converted into the blow -up boundary value problemu＂=e＂,limx→0＋u（x）=limx→1-u（x）=＋∞. Then, the exact nonnegative solution of the nonlinear two - point boundary value problems is showed. And it provides a new method of solving ordinary differential e- quations
出处
《吉林省教育学院学报》
2014年第4期151-152,共2页
Journal of Jilin Provincial Institute of Education
关键词
二阶非线性微分方程
边值问题
非负解
two - point nonlinear differential equation
boundary value problems
nonnegative solutions.
