Differential Equations

, Volume 49, Issue 8, pp 975–985 | Cite as

Multipoint problem for a class of evolution equations

  • O. V. Martynyuk
  • V. V. Gorodetskii
Partial Differential Equations


We prove the well-posed solvability of a nonlocal problem for evolution equations with nonnegative self-adjoint operators that have discrete spectrum and with boundary conditions in the space of linear continuous functionals of the type of ultra-distributions identified with formal Fourier series.


Evolution Equation Boundary Element Discrete Spectrum Generalize Element Convolution Operator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Gorbachuk, V.I., On the Solvability of the Dirichlet Problem for a Second-Order Operator-Differential Equation in Various Spaces, in Pryamye i obratnye zadachi spektral’noi teorii differentsial’nykh operatorov: Sb. nauch. trudov (Direct and Inverse Problems of the Spectral Theory of Differential Operators), Kiev: Akad. Nauk Ukrain. SSR, Inst. Mat., 1985, pp. 8–22.Google Scholar
  2. 2.
    Gorodets’kii, V.V., Mnozhini pochatkovikh znachen’ gladkikh rozv’yazkiv diferentsial’no-operatornikh rivnyan’ parabolichnogo tipu (Sets of Boundary Values of Smooth Solutions of Differential-Operator Equations of the Parabolic Type), Chernivtsi, 1998.Google Scholar
  3. 3.
    Babenko, K.I., On a New Problem of Quasi-Analyticity and on the Fourier Transform of Entire Functions, Tr. Mosk. Mat. Obs., 1956, vol. 5, pp. 523–542.MathSciNetzbMATHGoogle Scholar
  4. 4.
    Gorodets’kii, V.V., Zadacha Koshi dlya evolyutsiinikh rivnyan’ neskinchennogo poryadku (Cauchy Problem for Infinite-Order Evolution Equations), Chernivtsi, 2005.Google Scholar
  5. 5.
    Gorbachuk, V.I. and Gorbachuk, M.L., Granichnye zadachi dlya differentsial’no-operatornykh uravnenii (Boundary Value Problems for Operator-Differential Equations), Kiev: Naukova Dumka, 1984.Google Scholar
  6. 6.
    Gelfand, I.M. and Shilov, G.E., Prostranstva osnovnykh i obobshchennykh funktsii (Spaces of Test and Generalized Functions), Moscow: Gosudarstv. Izdat. Fiz.-Mat. Lit., 1958.Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2013

Authors and Affiliations

  • O. V. Martynyuk
    • 1
  • V. V. Gorodetskii
    • 1
  1. 1.Chernovtsy National UniversityChernovtsyUkraine

Personalised recommendations