Abstract:
We consider stability problem of balance on nonlinear differential equations of the second type of the Liénard type. Investigations are carried out by means of constant-sign Lyapunov's functions for problems of stability, asymptotical stability (local and global) and instability. Implicitly we formulate a method of construction of constant-sign functions suitable for solving problems of stability of motion. Special attention is paid to a problem of non-asymptotical stablity, where we demonstrate possibilities of new assertions that rely upon a usage of constant-sign Lyapunov functions.
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