中文摘要：

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.

英文摘要：

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=＋∞.