Estimates for the periodic and semi-periodic eigenvalues of Hill's equation

DOI10.1017/S0308210500000536zbMath0977.34077OpenAlexW2148106828MaRDI QIDQ4526688

B. J. Harris, Haskız Coşkun

Publication date: 7 January 2002

Published in: Proceedings of the Royal Society of Edinburgh: Section A Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0308210500000536

zbMATH Keywords

spectral asymptoticsHill's equationnonsmooth potentialperiodic and semi-periodic boundary conditionsSturm-Liouville problems with continuous spectra

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Sturm-Liouville theory (34B24) Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions for ordinary differential operators (34L20) Special ordinary differential equations (Mathieu, Hill, Bessel, etc.) (34B30)

Related Items (8)

Inverse problem for Hill equation with jump conditions ⋮ On Green's function for boundary value problem with eigenvalue dependent quadratic boundary condition ⋮ Asymptotic approximations of eigenvalues and eigenfunctions for regular Sturm-Liouville problems ⋮ Asymptotics of eigenvalues for regular Sturm--Liouville problems with eigenvalue parameter in the boundary condition ⋮ A note on eigenvalue asymptotics for Hill's equation ⋮ Extremal values of smallest eigenvalues of Hill's operators with potentials in \(L^1\) balls ⋮ Instability intervals for Hill's equation with symmetric single-well potential ⋮ Some inverse results for Hill's equation

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