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

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

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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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
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