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...theorem on the stability of the first approximation to a fixed point of an autonomous system of differential equations (cf. [[Lyapunov stability|Lyapunov stabili ...eorem on the instability of the first approximation to a fixed point of an autonomous system of differential equations, cf. [[Lyapunov stability|Lyapunov stabili

...^0=1$, $J=t_1-t_0$). This statement admits a natural generalization to non-autonomous systems, problems with variable end-points and problems with restricted pha Admitting closed sets $U$, $X$ (in particular, these regions can be determined by systems of non-strict inequalities) makes the problem

vary, one gets regions of elastic strain, active plastic strain (loading) and passive strain (unlo differ. These regions should be determined in solving the problem;

for a trajectory of an autonomous system (1) to hit a set $ M $, The study of the evolution of the regions $ X( \theta , \cdot ) $