Asymptotic formulae for eigenvalues and eigenfunctions of q-Sturm-Liouville problems

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Asymptotic formulae for eigenvalues and eigenfunctions of q-Sturm-Liouville problems

Annaby, Mahmoud H.; Mansour, Zeinab S.

Mathematische Nachrichten, 03/2011, Volume: 284, Issue: 4

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We investigate the asymptotic behavior of the eigenvalues and the eigenfunctions of q‐Sturm‐Liouville eigenvalue problems. For this aim we study the asymptotic behavior of q‐trigonometric functions as well as fundamental sets of solutions of the associated second order q‐difference equation. As in classical Sturm‐Liouville theory, the eigenvalues behave like zeros of q‐trigonometric functions and the eigenfunctions behave like q‐trigonometric functions. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim

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