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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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