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

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.

PDF

___

1] Atkinson, F.V.: Asymptotics of an eigenvalue problem involving an interior singularity,ANL Proceedings, ANL-87-262(1988), 1-18.
[2] Atkinson, F.V and Fulton, C.T.: Asymptotics of the eigenvalue problems on a nite intervalwith one limit circle singularity, Proc. Royal Soc. Edinburgh, Sect. A99(1984), 51-70.
[3] Coskun, H.: Topics in the theory of periodic di erential equations, Ph.D. Dissertation,1994, 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, Amen House, Lon-don, 1932
[9] Weikard, R.: On Hill's equation with a singular complex-valued potential, Proc., LMS,76(1998),603-633.

ISSN: 1300-0098
Yayın Aralığı: Yılda 6 Sayı
Yayıncı: TÜBİTAK

Arşiv