Theorems of Bôcher's type for dynamic equations on time scales
The conditions are found that all solutions of a systems dynamic equations on time scales tends to finite limits as $t\to\infty$.
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arXiv subjects
Vladimir Burd
Publications and source records attributed to Vladimir Burd.
Kinks in the parametrically excited sine-Gordon equation and method of averaging
Parametrically excited sine-Gordon equation is considered. Excitation is a fast oscillating periodic function with zero mean. Technique of classical method of averaging enables to construct the averaged equations in a variety of assumptions about driving amplitude. The averaged equation possesses kinks solutions. The results can be applied to the study of movement of Bloch walls for ferromagnetic crystals in the presence of a rapidly oscillating magnetic field and to describe the fluxon dynamics in long Josephson junctions.
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Stability under constantly acting perturbations for difference equations and averaging
We consider the problem of closeness of solutions of an exact and an averaged difference equations on an infinite interval. Appropriate assertions are derived from one special theorem on the stability under constantly acting perturbations.
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Resonance vibration of impact oscillator with biharmonic excitation
We consider a damped impact oscillator subject to the action of a biharmonic force. The conditions for the existence and stability of almost periodic resonance solutions are investigated.
math.CA↗