Abstract
On the basis of periodic Ateb functions, in the resonance and nonresonance cases, we construct the asymptotic approximation of one-frequency solutions of a boundary-value problem for a nonlinear nonautonomous equation.
This is a preview of subscription content, log in via an institution to check access.
References
Yu. A. Mitropol’skii and B. I. Moseenkov, Asymptotic Solutions of Partial Differential Equations [in Russian], Vyshcha Shkola Kiev (1976).
B. I. Sokil, “On a method for construction of one-frequency solutions of a nonlinear wave equation,” Ukr. Mat. Zh., 46, No. 6, 782–785 (1994).
B. I. Sokil, “Construction of one-frequency solutions of certain boundary-value problems for a nonautonomous wave equation,” Ukr. Mat. Zh., 46, No. 9, 1275–1279 (1994).
P. M. Senyk, “Inversion of the incomplete Beta function,” Ukr. Mat. Zh., 21, No. 3, 325–333 (1969).
N. N. Moiseev, Asymptotic Methods of Nonlinear Mechanics [in Russian], Nauka, Moscow (1969).
Additional information
“L’vivs’ka Politeknika” University, Lviv. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 11, pp. 1580–1583, November, 1997.
Rights and permissions
About this article
Cite this article
Sokil, B.I. On asymptotic approximation of a solution of a boundary-value problem for a nonlinear nonautonomous equation. Ukr Math J 49, 1777–1781 (1997). https://doi.org/10.1007/BF02487518
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02487518