Abstract
We obtain asymptotic formulas for the values of second-order differential operators with the coefficient of bounded variation depending on the spectral parameter. We give a counterexample showing that the requirement of boundedness for the variation is essential for the preservation of the error of the so-obtained asymptotic formulas.
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Original Russian Text Copyright © 2010 Trynin A. Yu.
The author was supported by the Russian Foundation for Basic Research (Grant 04-01-00060).
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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 51, No. 3, pp. 662–675, May–June, 2010.
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Trynin, A.Y. Asymptotic behavior of the solutions and nodal points of Sturm-Liouville differential expressions. Sib Math J 51, 525–536 (2010). https://doi.org/10.1007/s11202-010-0055-y
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DOI: https://doi.org/10.1007/s11202-010-0055-y