Differential Equations

, Volume 49, Issue 10, pp 1274–1281 | Cite as

Gellerstedt problem for a differential-difference equation of mixed type with advanced-retarded multiple deviations of the argument

  • A. N. Zarubin
Partial Differential Equations


We consider the Gellerstedt problem for an equation of mixed type with the Lavrent’ev-Bitsadze operator in the leading part and with advanced-retarded multiple deviations of the argument in the derivatives and the function. We prove the uniqueness theorem for the problem without restrictions on the deviation value. The problem is uniquely solvable. We derive closed-form integral representations of the solutions.


Differential Equation Partial Differential Equation Ordinary Differential Equation Cauchy Problem Functional Equation 
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  1. 1.
    Zarubin, A.N., Uravneniya smeshannogo tipa s zapazdyvayushchim argumentom (Equations of Mixed Type with Retarded Argument), Orel, 1997.Google Scholar
  2. 2.
    Ter-Krikorov, A.M. and Shabunin, M.I., Kurs matematicheskogo analiza (A Course in Mathematical Analysis), Moscow: Nauka, 1988.zbMATHGoogle Scholar
  3. 3.
    Agranovich, M.S., Obobshchennye funktsii (Generalized Functions), Moscow, 2008.Google Scholar
  4. 4.
    Gakhov, F.D. and Cherskii, Yu.I., Uravneniya tipa svertki (Equations of Convolution Type), Moscow: Nauka, 1978.zbMATHGoogle Scholar
  5. 5.
    Zarubin, A.N., A Boundary Value Problem for an Equation of Mixed Type with a Differential-Difference Operator, Differ. Uravn., 2011, vol. 47, no. 10, pp. 1439–1445.MathSciNetGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2013

Authors and Affiliations

  • A. N. Zarubin
    • 1
  1. 1.Orel State UniversityOrelRussia

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