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On generalized solutions of differential equations with several operator coefficients

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Ukrainian Mathematical Journal Aims and scope

We prove a theorem on the smoothness of generalized solutions of ordinary differential equations with several operator coefficients.

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References

  1. 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).

  2. M. L. Gorbachuk, “On representation of positive-definite operator functions,” Ukr. Mat. Zh., 17, No. 2, 29–46 (1965).

    Article  MATH  Google Scholar 

  3. 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).

  4. 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).

  5. 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).

  6. 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).

  7. M. L. Gorbachuk and V. I. Gorbachuk, Boundary-Value Problems for Differential Operator Equations [in Russian], Naukova Dumka, Kiev (1994).

    Google Scholar 

  8. A. N. Kochubei, “Fundamental solutions of differential-operator equations,” Differents. Uravn., 13, No. 9, 1588–1597 (1977).

    Google Scholar 

  9. Yu. M. Berezanskii, G. F. Us, and Z. G. Sheftel’, Functional Analysis [in Russian], Vyshcha Shkola, Kiev (1990).

  10. E. Kamke, Differentialgleichungen Lösungsmethoden und Lösungen, Akademische Verlagsgesellschaft Geest, Leipzig (1959).

  11. J. F. Treves, Lectures on Linear Partial Differential Equations with Constant Coefficients, Instituto de Matem´atica Pura e Aplicada, Rio de Janeiro (1961).

  12. Yu. L. Daletskii and M. G. Krein, Stability of Solutions of Differential Equations in a Banach Space [in Russian], Nauka, Moscow (1970).

    Google Scholar 

  13. M. Yu. Tsar’kov, “Solvability of differential equations with operator coefficients,” J. Math. Sci., 103, No. 1, 131–134 (2001).

    Article  MathSciNet  Google Scholar 

  14. 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).

    MathSciNet  MATH  Google Scholar 

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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 64, No. 6, pp. 860–864, June, 2012.

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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

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  • DOI: https://doi.org/10.1007/s11253-012-0694-1

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