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

Sheipak, I. A.; Vladimirov, A. A.

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

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Description

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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