Indefinite Sturm--Liouville problem for some classes of self-similar singular weights

I. A. Sheipak; A. A. Vladimirov

paper

Indefinite Sturm--Liouville problem for some classes of self-similar singular weights

arXiv:math/0507017

Abstract

We study the Sturm-Liouville problem $- y^{''} - ρ y = 0$ , $y (0) = y (1) = 0$ . $ρ$ is a generalized derivative of function $P \in L_{2} [0, 1]$ . For self-similar $P$ asymptotic formulas for eigenvalues are obtained. In this paper we consider two cases of self-similarity of $P$ : 1) arithmetic degenerate, and 2) non-arithmetic.

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