This is a preview of subscription content, log in via an institution to check access.
Literature Cited
N. N. Bogolyubov and Yu. A. Mitropol'skii, Asymptotic Methods in the Theory of Nonlinear Oscillations [in Russian], Gostekhizdat, Moscow (1955).
M. A. Krasnosel'skii, P. P. Zabreiko, E. I. Pustyl'nik, and P. E. Sobolevskii, Integral Operators in the Space of Summable Functions [in Russian], Nauka, Moscow (1966).
S. G. Krein, Linear Differential Equations in Banach Spaces [in Russian], Nauka, Moscow (1967).
V. Sh. Burd, P. P. Zabreiko, Yu. S. Kolesov, and M. A. Krasnosel'skii, “Averaging principle and bifurcation of almost periodic functions,” Dokl. Akad. Nauk SSSR,187, No. 6, 1219–1221 (1969).
I. B. Simonenko, “Proof of the averaging method for abstract parabolic equations,” Matem. Sb.,83(123), No. 1, 53–61 (1970).
V. V. Zhikov, “Averaging principle for parabolic equations with a variable principal term,” Dokl. Akad. Nauk SSSR,208, No. 1, 32–35 (1973).
I. B. Simonenko, “Proof of the averaging method for the convection problem in a field of rapidly oscillating forces and for other parabolic equations,” Matem. Sb.,87(129). 236–253 (1972).
Yu. L. Daletskii and M. G. Krein, Stability of Solutions of Differential Equations in Banach Space [in Russian], Nauka, Moscow (1970).
M. A. Krasnosel'skii, The Operator of Shift along the Trajectories of Differential Equations [in Russian], Nauka, Moscow (1966).
Additional information
Translated from Sibirskii Matematicheskii Zhurnal, Vol. 17, No. 5, pp. 1058–1068, September–October, 1976.
Rights and permissions
About this article
Cite this article
Levenshtam, V.B. The averaging method and bifurcation of bounded solutions of abstract parabolic equations. Sib Math J 17, 781–790 (1976). https://doi.org/10.1007/BF00966378
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00966378