Abstract:

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 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=+∞.

Key words: ordinary differential equation with initial value, existence and uniqueness, convolution approximation, Bihari’s inequality