LIMITING PERIODIC MOTIONS WITH RESONANCE IN SYSTEMS DESCRIBED BY VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS |
| 4 | |
| 2011 |
| scientific article | 531.1 | ||
| 2488-2489 |
| Motions which tend to periodic oscillations with time are considered. The critical case of a pair of pure imaginary roots is analyzed by the first Lyapunov's method for equations with analytical nonlinear parts and Lyapunov's constant g3 ? 0. The existence of a family of limiting periodic solutions is proved for the case when the frequency of external small perturbations coincides with the fundamental frequency of the linearized unperturbed system. |
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