Asymptotic behavior of solutions of a nonlinear system in the critical case of q pairs of purely imaginary eigenvalues

作者：Grushkovskaya V; Zuyev A^*

来源：Nonlinear Analysis-Theory Methods & Applications, 2013, 80: 156-178.

DOI：10.1016/j.na.2012.10.007

• Asymptotic estimate
• Critical case
• Stability
• Lyapunov function

This paper is devoted to the stability problem of a nonlinear system in the critical case of q pairs of purely imaginary eigenvalues. The center manifold theory and the normal form method are exploited in this study. The main result of the paper is a power estimate for the solutions in the case when stability is ensured by third order forms. A Lyapunov function is constructed explicitly as a part of the proof of this estimate. The result obtained is illustrated by an example of a double pendulum with partial dissipation.

• 出版日期2013-3