Geodesic
Asymptotic formulae for the real eigenvalues of the Sturm--Liouville problem with two turning points
Izvestiya. Mathematics , Tome 65 (2001) no. 5, pp. 1003-1016.

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We consider the asymptotic behavior of the real spectrum of the indefinite Sturm-Liouville problem for large values of the spectral parameter and prove the existence of infinitely many asymptotic terms under the condition that the coefficients of the equation are analytic. 
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S. N. Tumanov. Asymptotic formulae for the real eigenvalues of the Sturm--Liouville problem with two turning points. Izvestiya. Mathematics , Tome 65 (2001) no. 5, pp. 1003-1016. http://geodesic.mathdoc.fr/item/IM2_2001_65_5_a5/

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