Geodesic
On the formula for the distribution of the eigenvalues of singular differential operators
Matematičeskie zametki, Tome 14 (1973) no. 3, pp. 361-368.

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In this note we construct exampLes of a function $q(x)$, which grows arbitrarily rapidly, and a function $q(x)$ ($c_1|x|^\alpha\le q(x)\le c_2|x|^\beta$, $\beta>\alpha>0$) such that for a Sturm–Liouville operator with the constructed potential functions $q(x)$, the classical formula for the number of eigenvalues of the operator that do not exceed $\lambda$ is not true. 
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     author = {M. Otelbaev and Ya. T. Sultanaev},
     title = {On the formula for the distribution of the eigenvalues of singular differential operators},
     journal = {Matemati\v{c}eskie zametki},
     pages = {361--368},
     publisher = {mathdoc},
     volume = {14},
     number = {3},
     year = {1973},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1973_14_3_a5/}
}
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M. Otelbaev; Ya. T. Sultanaev. On the formula for the distribution of the eigenvalues of singular differential operators. Matematičeskie zametki, Tome 14 (1973) no. 3, pp. 361-368. http://geodesic.mathdoc.fr/item/MZM_1973_14_3_a5/