Geodesic
On the oscillation theory of the Sturm–Liouville problem with singular coefficients
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 9, pp. 1609-1621

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The spectral Sturm–Liouville problem with distribution coefficients is examined. It is shown that the basic results concerning the number and the location of the zeros of eigenfunctions that are known in the smooth case remain valid in the general situation. The Chebyshev properties of systems of eigenfunctions are also investigated in the case where the weight function is positive. 
@article{ZVMMF_2009_49_9_a7,
     author = {A. A. Vladimirov},
     title = {On the oscillation theory of the {Sturm{\textendash}Liouville} problem with singular coefficients},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1609--1621},
     publisher = {mathdoc},
     volume = {49},
     number = {9},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_9_a7/}
}
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A. A. Vladimirov. On the oscillation theory of the Sturm–Liouville problem with singular coefficients. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 9, pp. 1609-1621. http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_9_a7/