We prove a theorem on the smoothness of generalized solutions of ordinary differential equations with several operator coefficients.
Similar content being viewed by others
References
O. B. Chernobai, “On generalized solutions of differential equations with operator coefficients,” Ukr. Mat. Zh., 58, No. 5, 715–720 (2006); English translation: Ukr. Math. J., 58, No. 5, 808–814 (2006).
M. L. Gorbachuk, “On representation of positive-definite operator functions,” Ukr. Mat. Zh., 17, No. 2, 29–46 (1965).
M. L. Gorbachuk and A. I. Kashpirovskii, “Weak solutions of differential equations in Hilbert space,” Ukr. Mat. Zh., 33, No. 4, 513–518 (1981); English translation: Ukr. Math. J., 33, No. 4, 392–396 (1981).
A. I. Kashpirovskii, Boundary Values of Solutions of Some Classes of Homogeneous Differential Equations in a Hilbert Space [in Russian], Candidate-Degree Thesis (Physics and Mathematics), Kiev (1981).
O. B. Chernobai, “Spectral representation for generalized operator-valued Toeplitz kernels,” Ukr. Mat. Zh., 57, No. 12, 1698–1710 (2005); English translation: Ukr. Math. J., 57, No. 12, 1995–2010 (2005).
Yu. M. Berezansky and O. B. Chernobai, “On the theory of generalized Toeplitz kernels,” Ukr. Mat. Zh., 52, No. 11, 1458–1472 (2000); English translation: Ukr. Math. J., 52, No. 11, 1661–1678 (2000).
M. L. Gorbachuk and V. I. Gorbachuk, Boundary-Value Problems for Differential Operator Equations [in Russian], Naukova Dumka, Kiev (1994).
A. N. Kochubei, “Fundamental solutions of differential-operator equations,” Differents. Uravn., 13, No. 9, 1588–1597 (1977).
Yu. M. Berezanskii, G. F. Us, and Z. G. Sheftel’, Functional Analysis [in Russian], Vyshcha Shkola, Kiev (1990).
E. Kamke, Differentialgleichungen Lösungsmethoden und Lösungen, Akademische Verlagsgesellschaft Geest, Leipzig (1959).
J. F. Treves, Lectures on Linear Partial Differential Equations with Constant Coefficients, Instituto de Matem´atica Pura e Aplicada, Rio de Janeiro (1961).
Yu. L. Daletskii and M. G. Krein, Stability of Solutions of Differential Equations in a Banach Space [in Russian], Nauka, Moscow (1970).
M. Yu. Tsar’kov, “Solvability of differential equations with operator coefficients,” J. Math. Sci., 103, No. 1, 131–134 (2001).
F. A. Akgun, “On the Green function of a second order differential equation with operator coefficient,” An. Univ. Oradea. Fasc. Mat., 13, 5–22 (2006).
Author information
Authors and Affiliations
Additional information
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 64, No. 6, pp. 860–864, June, 2012.
Rights and permissions
About this article
Cite this article
Chernobai, O.B. On generalized solutions of differential equations with several operator coefficients. Ukr Math J 64, 985–989 (2012). https://doi.org/10.1007/s11253-012-0694-1
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11253-012-0694-1