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Journals / Turkish Journal of Mathematics / 1999 / Cilt: 23 - Sayı: 2

Some asymptotic estimates for the instability intervals of Hill's equation

Haskız COŞKUN
Pages
265–279
Publication Date
2022-11-03
DOI
—
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⚡ TL;DR(Too Long; Didn't Read)

In this study, some asymptotic estimates for the length of the instability intervals of Hill's equation, y''(t)+($lambda$ -q(t))y(t)=0, are derived by means of an auxiliary eigenvalue problem under various assumptions on the Fourier coefficients of the potential q.

📌 3 Key Takeaways

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Objective & Hypothesis:In this study, some asymptotic estimates for the length of the instability intervals of Hill's equation, y''(t)+($lambda$ -q(t))y(t)=0, are derived by means of an auxiliary eigenvalue problem under various assumptions on the Fourier coefficients of the potential q.
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Key Findings & Data:In this study, some asymptotic estimates for the length of the instability intervals of Hill's equation, y''(t)+($lambda$ -q(t))y(t)=0, are derived by means of an auxiliary eigenvalue problem under various assumptions on the Fourier coefficients of the potential q.
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Conclusion & Impact:In this study, some asymptotic estimates for the length of the instability intervals of Hill's equation, y''(t)+($lambda$ -q(t))y(t)=0, are derived by means of an auxiliary eigenvalue problem under various assumptions on the Fourier coefficients of the potential q.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

In this study, some asymptotic estimates for the length of the instability intervals of Hill's equation, y''(t)+($lambda$ -q(t))y(t)=0, are derived by means of an auxiliary eigenvalue problem under various assumptions on the Fourier coefficients of the potential q.

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Cite This Article

COŞKUN, H. (2022). Some asymptotic estimates for the instability intervals of Hill's equation. Turkish Journal of Mathematics, Cilt: 23 - Sayı: 2, 265–279. https://ajindex.com/articles/608975

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References (3)

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  2. Northern Illinois University, Dekalb,Il., USA. [4] Eastham, M.S.P.:The spectral theory of periodic di erential equations, Scottish AcademicPress, Edingburgh, 1973. [5] Harris, B.J.: Asymptotics of eigenvalues for regular Sturm-Liouville problems, Royal Soc.Edinburgh Sect. A110(1988), 63-71. [6] Hochstadt, H.: On the determination of a Hill's Equation from its Spectrum, Arc. Rat.Mech. Anal.,19(1965), 353-362. [7] Ntinos, A. A.: Lengths of instability intervals of second order periodic di erential equations,Quart. J. Math. Oxford (2)27(1976), 387-394. [8] Titchmarsh, E.C.:The Theory of Functions, Oxford University Press,
  3. Amen House, Lon-don, 1932 [9] Weikard, R.: On Hill's equation with a singular complex-valued potential, Proc., LMS,76(1998),603-633.