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Hans Volkmer

Instability intervals of the Ince and Hill equations

Keywords: Hill’s equation, Ince’s equation, instability intervals

The paper investigates the length L_m of the m-th instability interval of the Hill equation (1 + εA(x))y′′ + εB(x)y′ + (λ + εC(x))y = 0 with A(x), B(x), C(x) being trigonometric polynomials. The leading term in the expansion of L_m in powers of the perturbation parameter ε is found. The results are extensions of earlier work of Levy and Keller (1963).

Analysis, Oldenbourg Wissenschaftsverlag

Print ISSN: 0174-4747
Volume: 25, 03/2005
Pages: 189 - 204

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