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Instability Intervals for Hill’s Equation with Symmetric Single-Well Potential

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Ukrainian Mathematical Journal Aims and scope

With the help of an auxiliary eigenvalue problem, we deduce some explicit estimates for the periodic and semiperiodic eigenvalues and the lengths of instability intervals for Hill’s equation with symmetric single-well potentials. We also establish bounds for the gaps in the sets of Dirichlet and Neumann eigenvalues.

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References

  1. H. Coşkun and B. J. Harris, “Estimates for the periodic and semiperiodic eigenvalues of Hill’s equations,” Proc. Roy. Soc. Edinburgh Sect. A, 130, 991–998 (2000).

    Article  MathSciNet  Google Scholar 

  2. H. Coşkun, “Some inverse results for Hill’s equation,” J. Math. Anal. Appl., 276, 833–844 (2002).

    Article  MathSciNet  Google Scholar 

  3. H. Coşkun, “On the spectrum of a second order periodic differential equation,” Rocky Mountain J. Math., 33, 1261–1277 (2003).

    Article  MathSciNet  Google Scholar 

  4. M. S. P. Eastham, The Spectral Theory of Periodic Differential Equations, Scottish Academic Press, Edinburgh; London (1973).

    MATH  Google Scholar 

  5. N. B. Haaser and J. A. Sullivan, Real Analysis, Van Nostrand Reinhold Co., New York (1991).

    MATH  Google Scholar 

  6. H. Hochstadt, “On the determination of a Hill’s equation from its spectrum,” Arch. Ration. Mech. Anal., 19, 353–362 (1965).

    Article  MathSciNet  Google Scholar 

  7. M. J. Huang, “The first instability interval for Hill equations with symmetric single well potentials,” Proc. Amer. Math. Soc., 125, 775–778 (1997).

    Article  MathSciNet  Google Scholar 

  8. M. J. Huang and T. M. Tsai, “The eigenvalue gap for one-dimensional Schrödinger operators with symmetric potentials,” Proc. Roy. Soc. Edinburgh Sect. A, 139, 359–366 (2009).

    Article  MathSciNet  Google Scholar 

  9. A. Ntinos, “Lengths of instability intervals of second order periodic differential equations,” Q. J. Math., 27, 387–394 (1976).

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Karadeniz Technical University, Trabzon, Turkey

    H. Coşkun, E. Başkaya & A. Kabataş

Authors
  1. H. Coşkun
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  2. E. Başkaya
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  3. A. Kabataş
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Correspondence to E. Başkaya.

Additional information

Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 71, No. 6, pp. 858–864, June, 2019.

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Coşkun, H., Başkaya, E. & Kabataş, A. Instability Intervals for Hill’s Equation with Symmetric Single-Well Potential. Ukr Math J 71, 977–983 (2019). https://doi.org/10.1007/s11253-019-01692-x

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  • DOI: https://doi.org/10.1007/s11253-019-01692-x

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