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On the spectral property of a Dirichlet problem with explosive factor. (English) Zbl 1034.34098
Summary: We evaluate asymptotic formulas for the eigenvalues, the eigenfunctions and the normalization numbers of some version of a Dirichlet problem in a finite interval with explosive factor.

34L20Asymptotic distribution of eigenvalues for OD operators
34B24Sturm-Liouville theory
Full Text: DOI
[1] Z.F.A. El-Raheem, The inverse problem on a finite interval for the Sturm--Liouville operator with discontinuous coefficient, Ph.D. Thesis, Baku, USSR, 1990
[2] El-Raheem, Z. F. A.: The scattering problem for the Sturm--Liouville equation with discontinuous weight coefficient. J. appl. Anal. 57, 333-339 (1995) · Zbl 0831.34033
[3] El-Raheem, Z. F. A.: On some trace formula for the Sturm--Liouville operator. J. pure math. Appl. 7, No. 1--2, 61-68 (1996) · Zbl 0880.34018
[4] El-Raheem, Z. F. A.: The inverse scattering problem for some singular Sturm--Liouville operator. J. pure math. Appl. 8, No. 2--3--4, 233-246 (1997) · Zbl 0911.34072
[5] Marchenko: Sturm--Liouville operator and application. (1986)
[6] Karaa, S.: Sharp estimates for the eigenvalues of some differential equation. SIAM J. Math. anal. 29, No. 5, 1279-1300 (1998) · Zbl 0914.34072
[7] Gasimov, M. G.; Levitan, B. M.: The definition of a differential equation by two spectrums. Ospekh. math. Nauk 19, No. 2, 3-63 (1964) · Zbl 0145.10903