Abstract:
This paper is concerned with parametric resonance under nonlinear periodic perturbations of differential equations which are abstract analogues of hyperbolic systems. A modification of the Krylov-Bogolyubov averaging method capable of circumventing the well-known small divisor problem is applied to reduce the description of solutions of perturbed equations at resonance to the study of autonomous dynamical systems in finite-dimensional spaces.
Bibliography: 28 titles.