Abstract
We study the solvability of a periodic problem for monotone differential inclusions and the behavior of its solutions as the parameter changes.
Similar content being viewed by others
References
V. I. Blagodatskikh and A. F. Filippov, “Differential inclusions and optimal control,”Tr. Mat. Inst. Akad. Nauk SSSR,169, 194–252 (1985).
V. L. Hatskevich,Differential Inclusions with Monotone Operators [in Russian], Preprint No 6-5-90, Voronezh University, Voronezh (1990).
A. I. Povolotski and E. A. Gango, “On the periodic solutions of differential equations with many-valued right-hand sides,”Uch. Zap. Leningr. Ped. Inst., Issue 541, 145–154 (1972).
M. G. Crandall and A. Pazy, “Non-linear evolution equations in Banach Spaces,”Isr. J. Math.,11, 52–54 (1972).
J.-P. Aubin and P. Ekeland,Applied Nonlinear Analysis [Russian translation], Mir, Moscow (1988).
V. Yu. Trubnikov and A. I. Perov,Differential Equations with Monotone Nonlinearities [in Russian], Nauka i Tekhnika, Minsk (1986).
A. N. Tikhonov, “System of differential equations with small parameters by the derivatives,”Mat. Sb.,31, No. 3, 575–586 (1952).
A. A. Tolstonogov,Differential Inclusions in Banach Space [in Russian], Nauka, Novosibirsk (1986).
Yu. A. Mitropol'skii,Averaging Method in Nonlinear Mechanics [in Russian], Naukova Dumka, Kiev (1979).
Author information
Authors and Affiliations
Additional information
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 5, pp. 694–703, May, 1993.
Rights and permissions
About this article
Cite this article
Khatskevich, V.L. Periodic solutions of monotone differential inclusions with fast and slow variables. Ukr Math J 45, 761–772 (1993). https://doi.org/10.1007/BF01058211
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01058211