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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]:
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Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, 2014, Issue 3(36), Pages 44–56
DOI: https://doi.org/10.14498/vsgtu1321 (Mi vsgtu1321) 		 
Differential Equations

On the Solvability of Boundary Value Problem for Mixed-type Equation with a Singular Coefficient

M. Kh. Ruziev

Institute of Mathematics, National University of Uzbekistan named by after Mirzo Ulugbek, Tashkent, 100125, Uzbekistan
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DOI: https://doi.org/10.14498/vsgtu1321
Abstract: In this paper we study a problem with conditions on the inner characteristic and on some parts of the degeneration line for mixed type equation with singular coefficient in unbounded domain. We prove the uniqueness of solution of the mentioned problem with the help of the extremum principle. The proof of the existence of solution is based on the theory of singular integral equations and Fredholm integral equations.
Keywords: principle of extremum, unique solvability, existence of solution, singular coefficient, integral equations, Wiener–Hopf equation, index equation, Fourier integral.
Original article submitted 25/III/2014
revision submitted – 18/IV/2014
Bibliographic databases:
Document Type: Article
UDC: 517.956.6
MSC: Primary 35M12; Secondary 35A01, 35A02
Language: Russian
Citation: M. Kh. Ruziev, “On the Solvability of Boundary Value Problem for Mixed-type Equation with a Singular Coefficient”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 3(36) (2014), 44–56
Citation in format AMSBIB
\Bibitem{Ruz14}
\by M.~Kh.~Ruziev
\paper On the Solvability of Boundary Value Problem for Mixed-type Equation with a Singular Coefficient
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2014
\vol 3(36)
\pages 44--56
\mathnet{http://mi.mathnet.ru/vsgtu1321}
\crossref{https://doi.org/10.14498/vsgtu1321}
\zmath{https://zbmath.org/?q=an:06968916}
\elib{https://elibrary.ru/item.asp?id=23085710}
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    		Вестник Самарского государственного технического университета. Серия: Физико-математические науки
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