On the Stability of the Zero Solution of a Second-Order Differential Equation under a Periodic Perturbation of the Center

  • A. A. DorodenkovEmail author


Small periodic perturbations of the oscillator \(\ddot x + {x^{2n}}\) sgn x = Y(t, x, \(\dot x\)) are considered, where n < 1 is a positive integer and the right-hand side is a small perturbation periodic in t, which is an analytic function in \(\dot x\) and x in a neighborhood of the origin. New Lyapunov-type periodic functions are introduced and used to investigate the stability of the equilibrium position of the given equation. Sufficient conditions for asymptotic stability and instability are given.


asymptotic stability small periodic perturbation oscillator 


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© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.St. Petersburg Electrotechnical University “LETI,”St. PetersburgRussia

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