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Medientyp:
E-Artikel
Titel:
The Lyapunov Stability for the Linear and Nonlinear Damped Oscillator with Time‐Periodic Parameters
Beteiligte:
Chu, Jifeng;
Xia, Ting
Erschienen:
Wiley, 2010
Erschienen in:
Abstract and Applied Analysis, 2010 (2010) 1
Sprache:
Englisch
DOI:
10.1155/2010/286040
ISSN:
1085-3375;
1687-0409
Entstehung:
Anmerkungen:
Beschreibung:
Let a(t), b(t) be continuous T‐periodic functions with . We establish one stability criterion for the linear damped oscillator x′′ + b(t)x′ + a(t)x = 0. Moreover, based on the computation of the corresponding Birkhoff normal forms, we present a sufficient condition for the stability of the equilibrium of the nonlinear damped oscillator x′′ + b(t)x′ + a(t)x + c(t)x2n−1 + e(t, x) = 0, where n ≥ 2, c(t) is a continuous T‐periodic function, e(t, x) is continuous T‐periodic in t and dominated by the power x2n in a neighborhood of x = 0.