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Remarks on the perturbation theory for problems of Mathieu type. (English. Russian original) Zbl 0541.34035

Russ. Math. Surv. 38, No. 4, 215-233 (1983); translation from Usp. Mat. Nauk 38, No. 4(232), 189-203 (1983).
The Mathieu problem is studied. An asymptotic Rayleigh-Schrödinger series of the perturbed simple eigenvalues as well as an asymptotic series of the perturbed multiple eigenvalues is constructed. The width of the parametric resonance zone in the Hill’s equation is studied. An estimate of the width of the resonance zones is obtained.
Reviewer: S.G.Hristova

MSC:

34E10 Perturbations, asymptotics of solutions to ordinary differential equations
34E05 Asymptotic expansions of solutions to ordinary differential equations
34D10 Perturbations of ordinary differential equations
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