Abstract
The autoresonance problem is to distinguish solutions with unboundedly increasing amplitude for model equations of principal resonance. At the level of formal constructions, the problem is solved by constructing an asymptotic solution in the form of a power series with constant coefficients. As is known, such a series represents the asymptotic behavior of the exact solution. However, for this solution to be related to the description of a physical phenomenon, the stability of the solution is required both with respect to perturbations of the initial data and with respect to the relatively constantly acting perturbations. These two properties are established using the Lyapunov function.
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