Abstract

We obtain a sufficient condition using two Lyapunov functions for the Lagrange instability with respect to part of the variables. We also obtain another sufficient condition for the Lagrange instability with respect to part of the variables; this condition uses one Lyapunov function and is an analog of the Chetaev theorem on the instability with respect to part of the variables. If the considered part of the variables coincides with the set of all variables, then the sufficient criterion with one Lyapunov function is a corollary of the sufficient criterion with two Lyapunov functions.

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