On the Stability of the Zero Solution of a Second-Order Differential Equation under a Periodic Perturbation of the Center
- Authors: Dorodenkov A.A.1
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Affiliations:
- St. Petersburg Electrotechnical University “LETI,”
- Issue: Vol 51, No 1 (2018)
- Pages: 31-35
- Section: Mathematics
- URL: https://journals.rcsi.science/1063-4541/article/view/185927
- DOI: https://doi.org/10.3103/S106345411801003X
- ID: 185927
Cite item
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.
About the authors
A. A. Dorodenkov
St. Petersburg Electrotechnical University “LETI,”
Author for correspondence.
Email: alex_meth@mail.ru
Russian Federation, St. Petersburg, 197376