Let be continuous -periodic functions with . We establish one stability criterion for the linear damped oscillator . 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 , where is a continuous -periodic function, is continuous -periodic in and dominated by the power in a neighborhood of .
Jifeng Chu. Ting Xia. "The Lyapunov Stability for the Linear and Nonlinear Damped Oscillator with Time-Periodic Parameters." Abstr. Appl. Anal. 2010 1 - 12, 2010. https://doi.org/10.1155/2010/286040