Asymptotic formulae for the real eigenvalues of the Sturm-Liouville problem with two turning points

Izvestiya Mathematics

Volumn 65, Issue 5, 2001, Pages 1003-1016

  Tumanov, S N ^a  

^a NONE

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Indexed keywords

EID: 4344698805     PISSN: 10645632     EISSN: 14684810     Source Type: Journal    
DOI: 10.1070/IM2001v065n05ABEH000360     Document Type: Article

References (6)

1. F. V. Atkinson and A. B. Mingarelli, "Asymptotics of the number of zeros and of the eigenvalues of general weighted Sturm-Liouville problems", J. Reine Angew. Math. 375 (1987), 380-393.
2. A. A. Dorodnitsyn, "Asymptotic laws of distribution of the eigenvalues for certain special forms of differential equations of the second order", Uspekhi Mat. Nauk 7:6 (1952), 3-96. (Russian)
3. A. V. D'yachenko, "Asymptotics of the eigenvalues of an indefinite Sturm-Liouville problem", Mat. Zametki 68 (2000), 139-1-13; English transl., Math. Notes 68 (2000), 120-124.
4. M. A. Evgrafov and M. V. Fedoryuk, "Asymptotic behavior of solutions of the equation w" - p(z,λ)w = 0 as λ → ∞ in the complex plane", Uspekhi Mat. Nauk 21:1 (1966), 3-50; English transl. in Russian Math. Surveys 21:1 (1966).
5. F. Olver, Asymptotics and special functions, Academic Press, New York 1974; reprint of 1974 original, A. K. Peters Ltd., Wellesley, MA 1997; Russian transl., Nauka, Moscow 1990.
6. M. V. Fedoryuk, Asymptotic methods for linear ordinary differential equations, Nauka, Moscow 1983. (Russian)