Abstract
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.
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References
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Original Russian Text © A.A. Dorodenkov, 2018, published in Vestnik Sankt-Peterburgskogo Universiteta: Matematika, Mekhanika, Astronomiya, 2018, Vol. 63, No. 1, pp. 41–46.
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Dorodenkov, A.A. On the Stability of the Zero Solution of a Second-Order Differential Equation under a Periodic Perturbation of the Center. Vestnik St.Petersb. Univ.Math. 51, 31–35 (2018). https://doi.org/10.3103/S106345411801003X
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DOI: https://doi.org/10.3103/S106345411801003X