常微分方程初值问题解的存在唯一性  

Existence and Uniqueness for the Solution of Ordinary Differential Equations with Initial Values

作　　者：罗环环 范胜君[1] 

机构地区：[1]中国矿业大学理学院,江苏徐州221116

出　　处：《吉林大学学报（理学版）》2015年第2期166-172,共7页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:11371362);江苏省青蓝工程中青年学术带头人专项基金(批准号:苏教师[2012]39号)

摘　　要：利用卷积逼近和Bihari不等式等工具,在函数f(t,y)满足关于y连续、弱单调、具有一般增长,f(t,0)在[0,T]上绝对可积且T<+∞或T=+∞的条件下,证明了常微分方程初值问题{y′(t)=f(t,y(t)),t∈[0,T],y(0)=a解的存在唯一性.By virtue of the convolution approximation,Bihari＇s inequality and other tools,we put forward and proved that the solution of the following ordinary differential equation{y′（t）=f（t,y（t））, t∈ [0,T],y（0）=a exists and is unique under the conditions that the function f（t,y）satisfies a continuity condition,a weak monotonicity condition and a general growth condition in y,and the f（t,0）is absolutely integrable on[0,T]with T＋∞ or T=＋∞.

关 键 词：常微分方程初值问题 存在唯一性 卷积逼近 BIHARI不等式 

分 类 号：O175.1[理学—数学]