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On the solvability of a linear homogeneous functional-differential equation of point type

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Abstract

We consider the Cauchy problem for a linear homogeneous functional-differential equation of point type on the real line. For the case of a one-dimensional equation, we obtain sufficient conditions for the existence and uniqueness of a solution with a prescribed order of growth. The spectral properties of the operator generated by the right-hand side of such an equation are studied in detail. The study relies upon a formalism based on the group properties of such equations.

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References

  1. El’sgol’ts, L.E. and Norkin, S.B., Vvedenie v teoriyu differentsial’nykh uravnenii s otklonyayushchimsya argumentom (Introduction to the Theory of Differential Equations with Deviating Argument), Moscow: Nauka, 1971.

    Google Scholar 

  2. Arutyunov, A.V., Soobshch. Akad. Nauk Gruz. SSR, 1986, vol. 122, no. 2, pp. 265–268.

    MATH  MathSciNet  Google Scholar 

  3. Beklaryan, L.A., Dokl. Akad. Nauk SSSR, 1991, vol. 317, no. 6, pp. 1289–1294.

    MathSciNet  Google Scholar 

  4. Beklaryan, L.A., Sovrem. Mat. Fundam. Napravl., 2004, vol. 8, pp. 3–147.

    MATH  MathSciNet  Google Scholar 

  5. Trenogin, V.A., Funktsional’nyi analiz (Functional Analysis), Moscow: Nauka, 1980.

    Google Scholar 

  6. Rudin, W., Functional Analysis, New York: McGraw-Hill, 1973. Translated under the title Funktsional’nyi analiz, Moscow: Mir, 1975.

    MATH  Google Scholar 

  7. Markushevich, A.I. and Markushevich, L.A., Vvedenie v teoriyu analiticheskikh funktsii (Introduction to the Theory of Analytic Functions), Moscow: Prosveshchenie, 1977.

    Google Scholar 

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Authors and Affiliations

  1. Central Economics and Mathematics Institute, Russian Academy of Sciences, Moscow, Russia

    L. A. Beklaryan & M. B. Kruchenov

Authors
  1. L. A. Beklaryan
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  2. M. B. Kruchenov
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Additional information

Original Russian Text © L.A. Beklaryan, M.B. Kruchenov, 2008, published in Differentsial’nye Uravneniya, 2008, Vol. 44, No. 4, pp. 435–445.

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Beklaryan, L.A., Kruchenov, M.B. On the solvability of a linear homogeneous functional-differential equation of point type. Diff Equat 44, 453–463 (2008). https://doi.org/10.1134/S0012266108040010

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  • DOI: https://doi.org/10.1134/S0012266108040010

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