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We consider a balance stability problem for the second order nonlinear differential equations of the Liénard type. Investigations are carried out by means of constant-sign Lyapunov functions for problems of… Click to show full abstract
We consider a balance stability problem for the second order nonlinear differential equations of the Liénard type. Investigations are carried out by means of constant-sign Lyapunov functions for problems of stability, asymptotical stability (local and global), and instability. We implicitly formulate a method of construction of constant-sign functions suitable for solving problems of motion stability. Special attention is paid to a problem of non-asymptotical stability, where we demonstrate possibilities of new assertions that rely upon a usage of constant-sign Lyapunov functions.
Journal Title: Russian Mathematics
Year Published: 2018
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