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

Abstract

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.