Abstract
We consider the second order ordinary differential equations whose coefficients of the unknowns contain smooth and rapidly oscillating summands proportional to the positive powers of the oscillation frequency. The complete asymptotic expansions are constructed and justified of solutions to the Cauchy problem.
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Original Russian Text Copyright © 2010 Krutenko E. V. and Levenshtam V. B.
The second author was supported in part by the Southern Mathematical Institute of the Vladikavkaz Scientific Center.
Rostov-on-Don. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 51, No. 1, pp. 74–89, January–February, 2010.
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Krutenko, E.V., Levenshtam, V.B. Asymptotics of a solution to a second order linear differential equation with large summands. Sib Math J 51, 57–71 (2010). https://doi.org/10.1007/s11202-010-0008-5
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DOI: https://doi.org/10.1007/s11202-010-0008-5