Abstract
By using special periodic Ateb-functions, we construct asymptotic representations of one-frequency solutions of boundary-value problems for a nonautonomous wave equation.
This is a preview of subscription content, log in via an institution to check access.
References
N. N. Bogolyubov and Yu. A. Mitropol'skii,Asymptotic Methods in the Theory of Nonlinear Oscillations [in Russian], Nauka, Moscow (1974).
Yu. A. Mitropol'skii and B. I. Moseenkov,Asymptotic Solutions of Partial Differential Equations [in Russian], Vyshcha Shkola, Kiev (1976).
A. D. Myshkis and A. M. Filimonov, “Periodic oscillations in nonlinear one-dimensional continuum,” in:Proceedings of the 9th International Conference on Nonlinear Oscillations [in Russian], Vol. 1, Naukova Dumka, Kiev (1984), pp. 274–276.
B. I. Sokil and A. F. Barvinskii, “On the asymptotic solution of a nonlinear boundary-value problem,”Dokl. Akad. Nauk Ukr. SSR, Ser. A, No. 1, 22–26 (1980).
B. I. Sokil and A. F. Barvinskii, “Asymptotic method and periodic Ateb-functions in the investigation of wave equations,”Differents. Uravn.,18, No. 4, 718–721 (1982).
P. M. Senik, “Inversion of an incomplete beta-function,”Ukr. Mat. Zh.,21, No. 3, 325–333 (1969).
Author information
Authors and Affiliations
Additional information
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 9, pp. 1275–1279, September, 1994.
Rights and permissions
About this article
Cite this article
Sokil, B.I. Construction of one-frequency solutions of boundary-value problems for a nonautonomous wave equation. Ukr Math J 46, 1404–1409 (1994). https://doi.org/10.1007/BF01059432
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01059432