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

Small periodic perturbations of the oscillator x ¨ + x 2 n sgn x = Y ( t , x , 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 x ˙ and x in a neighborhood of the origin. New Lyapunov-type peri...

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Bibliographic Details
Published in:Vestnik, St. Petersburg University. Mathematics St. Petersburg University. Mathematics, 2018, Vol.51 (1), p.31-35
Main Author: Dorodenkov, A. A.
Format: Article
Language:English
Subjects:
Analysis
Analytic functions
Differential equations
Mathematics
Mathematics and Statistics
Periodic functions
Periodic variations
Stability
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Summary:Small periodic perturbations of the oscillator x ¨ + x 2 n sgn x = Y ( t , x , 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 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.
ISSN:1063-4541
1934-7855
DOI:10.3103/S106345411801003X