A necessary and sufficient condition for the global asymptotic stability of damped half-linear oscillators

DOI10.1007/s10474-012-0259-7zbMath1299.34193OpenAlexW2066449918MaRDI QIDQ2250804

Jitsuro Sugie, Saori Hata

Publication date: 21 July 2014

Published in: Acta Mathematica Hungarica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10474-012-0259-7

zbMATH Keywords

global asymptotic stabilityhalf-linear differential equationRiccati transformationgrowth conditionPrüfer transformationdamped oscillator

Mathematics Subject Classification ID

Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Global stability of solutions to ordinary differential equations (34D23) Attractors of solutions to ordinary differential equations (34D45)

Related Items

Integral condition for oscillation of half-linear differential equations with damping

Cites Work

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• Global asymptotic stability for half-linear differential systems with generalized almost periodic coefficients
• Global asymptotic stability for damped half-linear oscillators
• Asymptotic stability of the equilibrium of the damped oscillator
• Global asymptotic stability for nonlinear systems of differential equations and applications to reactor dynamics
• Stability theory by Liapunov's direct method
• Attractivity of the origin for the equation \(\ddot x+f(t,x,\dot x)|\dot x|^\alpha x+g(x)=0\)
• Precise damping conditions for global asymptotic stability for nonlinear second order systems
• A necessary and sufficient condition for the asymptotic stability of the damped oscillator
• Stability of dynamical systems. Continuous, discontinuous, and discrete systems
• Differential equations: Stability, oscillations, time lags
• Non-uniform asymptotic stability for the damped linear oscillator
• Uniform global asymptotic stability for half-linear differential systems with time-varying coefficients
• ASYMPTOTIC STABILITY OF x″+a(t)x′+x=0
• On stability of linear time-varying second-order differential equations
• Asymptotic stability of two dimensional systems of linear difference equations and of second order half-linear differential equations with step function coefficients
• Integral conditions on the uniform asymptotic stability for two-dimensional linear systems with time-varying coefficients
• CONVERGENCE OF SOLUTIONS OF TIME-VARYING LINEAR SYSTEMS WITH INTEGRABLE FORCING TERM
• On the asymptotic stability of oscillators with unbounded damping
• On the asymptotic stability for a two-dimensional linear nonautonomous differential system
• Integral conditions on the asymptotic stability for the damped linear oscillator with small damping
• Liapunov functions and stability in control theory