Lyapunov stability and boundedness of solutions of reversible second order differential equations. (Russian) Zbl 1199.34256
The author considers differential equations of second order which may be treated as a small periodic reversible perturbation of a nonlinear oscillator with odd restoring force. The stability of the zero solution is proved. Also, the boundedness of solutions is proved under some conditions imposed on the perturbations. The analysis is based on KAM-theory.
Reviewer: I. T. Selezov (Kyïv)
MSC:
| 34D20 | Stability of solutions to ordinary differential equations |
| 34C15 | Nonlinear oscillations and coupled oscillators for ordinary differential equations |
| 34D10 | Perturbations of ordinary differential equations |
| 34C14 | Symmetries, invariants of ordinary differential equations |
| 34C11 | Growth and boundedness of solutions to ordinary differential equations |
