一类一阶常微分方程初值问题的无穷多解性

Multi-solutions to a Class of First Order Ordinary DE with Initial Value

应用分离变量法,得到了一类一阶微分方程初值问题u′(t)=b(t)f(u(t)),t>0,u(0)=0存在无穷多个解的充分必要条件.并给出了全部解.

From the variable-separating method and inverse function theorem, a sufficient and necessary condition for the existence of infinitely many solutions to a class of first order ordinary differential equations, u′（t）=b（t）f（u））,t〉0, with initial value, u（0）=0, is derived. Some ex4mples are show here and their all solutions are given.