Geodesic
Asymptotic analysis of the parametric instability of nonlinear hyperbolic equations
Sbornik. Mathematics, Tome 208 (2017) no. 8, pp. 1088-1112

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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.
Keywords: hyperbolic equations, parametric resonance, averaging method. 
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     author = {V. S. Belonosov},
     title = {Asymptotic analysis of the parametric instability of nonlinear hyperbolic equations},
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     url = {http://geodesic.mathdoc.fr/item/SM_2017_208_8_a1/}
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V. S. Belonosov. Asymptotic analysis of the parametric instability of nonlinear hyperbolic equations. Sbornik. Mathematics, Tome 208 (2017) no. 8, pp. 1088-1112. http://geodesic.mathdoc.fr/item/SM_2017_208_8_a1/