Geodesic
On inverse Sturm--Liouville problems on a finite segment
Izvestiya. Mathematics , Tome 1 (1967) no. 5, pp. 923-934

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A necessary and sufficient condition for reconstructing the differential operator $-y''+dF\cdot y$, where $F$ is a function of bounded variation, from the spectra of two boundary value problems on the segment $[0,\pi]$, is established in this paper. 
@article{IM2_1967_1_5_a1,
     author = {V. V. Zhikov},
     title = {On inverse {Sturm--Liouville} problems on a finite segment},
     journal = {Izvestiya. Mathematics },
     pages = {923--934},
     publisher = {mathdoc},
     volume = {1},
     number = {5},
     year = {1967},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1967_1_5_a1/}
}
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V. V. Zhikov. On inverse Sturm--Liouville problems on a finite segment. Izvestiya. Mathematics , Tome 1 (1967) no. 5, pp. 923-934. http://geodesic.mathdoc.fr/item/IM2_1967_1_5_a1/