On the stability of the zero solution of a differential equation of the second order in a critical case

DOI10.1134/S1063454121040051zbMath1500.34048OpenAlexW4285355557WikidataQ115247664 ScholiaQ115247664MaRDI QIDQ2668892

A. A. Dorodenkov

Publication date: 9 March 2022

Published in: Vestnik St. Petersburg University. Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s1063454121040051

zbMATH Keywords

stabilityoscillatorLyapunov constantsmall periodic perturbations

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Stability of solutions to ordinary differential equations (34D20) Perturbations of ordinary differential equations (34D10) Nonautonomous smooth dynamical systems (37C60)

Cites Work

• Stability and bifurcation of invariant tori from an equilibrium state of an essentially nonlinear second-order differential equation
• Stability and bifurcation for periodic perturbations of the equilibrium of an oscillator with infinite or infinitesimal oscillation frequency
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