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Izv. Akad. Nauk SSSR Ser. Mat., 1967, Volume 31, Issue 3, Pages 543–562 (Mi izv2552)  

This article is cited in 1 scientific paper (total in 1 paper)

A linear boundary value problem for a system of composite partial differential equations

A. D. Dzhuraev


Abstract: A two-variable system of first-order partial differential equations is investigated which has, in the region under consideration, one family of real characteristics and two families of imaginary characteristics. A general linear boundary value problem for the system is studied. It is proved that if a certain condition is imposed on the coefficients in the boundary conditions, there is only a finite number of linearly independent solutions of the homogeneous problem and of the adjoint homogeneous problem. A formula for the index of the above problem is derived and a necessary and sufficient condition for the solvability of the inhomogeneous problem is obtained in terms of the homogeneous adjoint problem.

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English version:
Mathematics of the USSR-Izvestiya, 1967, 1:3, 525–543

Bibliographic databases:

UDC: 517.9
MSC: 35J25, 35Q15, 45E05
Received: 14.07.1965

Citation: A. D. Dzhuraev, “A linear boundary value problem for a system of composite partial differential equations”, Izv. Akad. Nauk SSSR Ser. Mat., 31:3 (1967), 543–562; Math. USSR-Izv., 1:3 (1967), 525–543

Citation in format AMSBIB
\Bibitem{Dzh67}
\by A.~D.~Dzhuraev
\paper A linear boundary value problem for a system of composite partial differential equations
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1967
\vol 31
\issue 3
\pages 543--562
\mathnet{http://mi.mathnet.ru/izv2552}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=223762}
\zmath{https://zbmath.org/?q=an:0163.12502}
\transl
\jour Math. USSR-Izv.
\yr 1967
\vol 1
\issue 3
\pages 525--543
\crossref{https://doi.org/10.1070/IM1967v001n03ABEH000570}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Martin Costabel, “A contribution to the theory of singular integral equations with carleman shift”, Integr equ oper theory, 2:1 (1979), 11  crossref  mathscinet  zmath
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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