## The use of Lyapunov functions in uniqueness and nonuniqueness theorems.(English)Zbl 1090.34503

In the paper there is given a survey of nonuniqueness theorems for the initial value problem $x'=f(t,x)\,\qquad x(t_0)=x_0$ where $$f=(f_1,\dots ,f_n)$$, $$x=(x_1,\dots ,x_n)$$, $$x_0=(x_{01},\dots , x_{0n})$$. The contribution is devoted to using Lyapunov functions in nonuniqueness theorems.

### MSC:

 34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations 34A34 Nonlinear ordinary differential equations and systems
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