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

I. A. Sheipak·A. A. Vladimirov
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Abstract

We study the Sturm-Liouville problem $-y''-ρy=0$, $y(0)=y(1)=0$. $ρ$ 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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I. A. Sheipak, A. A. Vladimirov. 2005-07-01. Indefinite Sturm--Liouville problem for some classes of self-similar singular weights. https://arxiv.org/abs/math/0507017

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