Geodesic
Estimates for the first eigenvalue of the Sturm--Liouville problem with potentials in weighted spaces
Trudy Seminara im. I.G. Petrovskogo, Trudy Seminara imeni I. G. Petrovskogo, Tome 32 (2019) no. 32, pp. 162-190

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We consider the Sturm–Liouville problem on the interval $[0,1]$ with the Dirichlet boundary conditions and a weighted integral condition on the potential function, which allows the potential to have singularities of different orders at the end-points. For some values of the parameters of the weight functions, estimates are obtained for the first eigenvalue of this problem, and a method is proposed for finding precise bounds for this eigenvalue in some cases. 
@article{TSP_2019_32_32_a7,
     author = {S. S. Ezhak and M. Yu. Telnova},
     title = {Estimates for the first eigenvalue of the {Sturm--Liouville} problem with potentials in weighted spaces},
     journal = {Trudy Seminara im. I.G. Petrovskogo},
     pages = {162--190},
     publisher = {mathdoc},
     volume = {32},
     number = {32},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TSP_2019_32_32_a7/}
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S. S. Ezhak; M. Yu. Telnova. Estimates for the first eigenvalue of the Sturm--Liouville problem with potentials in weighted spaces. Trudy Seminara im. I.G. Petrovskogo, Trudy Seminara imeni I. G. Petrovskogo, Tome 32 (2019) no. 32, pp. 162-190. http://geodesic.mathdoc.fr/item/TSP_2019_32_32_a7/