Geodesic
On the Eigenvalues and Eigenfunctions of the Sturm--Liouville Operator with a Singular Potential
Matematičeskie zametki, Tome 69 (2001) no. 2, pp. 277-285

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In this paper we consider the Sturm–Liouville operators generated by the differential expression $-y+q(x)y$ and by Dirichlet boundary conditions on the closed interval $[0,\pi]$. Here $q(x)$ is a distribution of first order, i.e., $\int q(x)dx\in L_2[0,\pi]$. Asymptotic formulas for the eigenvalues and eigenfunctions of such operators which depend on the smoothness degree of $q(x)$ are obtained. 
@article{MZM_2001_69_2_a10,
     author = {A. M. Savchuk},
     title = {On the {Eigenvalues} and {Eigenfunctions} of the {Sturm--Liouville} {Operator} with a {Singular} {Potential}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {277--285},
     publisher = {mathdoc},
     volume = {69},
     number = {2},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2001_69_2_a10/}
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A. M. Savchuk. On the Eigenvalues and Eigenfunctions of the Sturm--Liouville Operator with a Singular Potential. Matematičeskie zametki, Tome 69 (2001) no. 2, pp. 277-285. http://geodesic.mathdoc.fr/item/MZM_2001_69_2_a10/