Abstract
We find the eigenvalues and eigenfunctions of two nonlocal problems for a mixed-type equation with the singular coefficients of lower-order terms.
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Salakhitdinov M. S. and Urinov A. K., “On a boundary value problem for an equation of mixed type with nonsmooth degeneration lines,” Dokl. Akad. Nauk SSSR, 262, No. 3, 539–541 (1982).
Salakhitdinov M. S. and Khasanov A., “The Tricomi problem for an equation of mixed type with a nonsmooth degeneration line,” Differential Equations, 19, No. 1, 94–101 (1983).
Moiseev E. I., “Solution of the Tricomi problem in special domains,” Differential Equations, 26, No. 1, 83–91 (1990).
Moiseev E. I., “Some boundary value problems for mixed-type equations,” Differential Equations, 28, No. 1, 105–115 (1992).
Ponomarev S. M., Spectral Theory of a Basic Boundary-Value Problem for the Lavrent’ev-Bitsadze Equation of Mixed Type [in Russian], Diss. Dokt. Fiz.-Mat. Nauk, Moscow (1981).
Kal’menov T. S., “The spectrum of Tricomi’s problem for the Lavrent’ev-Bitsadze equation,” Differential Equations, 13, No. 8, 984–989 (1977).
Kerimkulov S. E., “An eigenvalue problem for an equation of mixed type,” Izv. Akad. Nauk Kaz. SSR Ser. Fiz.-Mat., 5, 20–23 (1986).
Sabitov K. B. and Khasanov S. L., “Solution of the Tricomi-Neumann problem for the Lavrent’ev-Bitsadze equation by the method of spectral analysis,” Izv. KBNTs RAN, No. 1, 84–93 (2002).
Sabitov K. B. and Il’yasov R. R. “Spectral problems for the mixed-type operator with singular coefficient,” in: The International Conference “Partial Differential Equations and Related Problems of Analysis and Informatics,” 2004, Vol. 1, pp. 266–269.
Urinov A. K. and Tozhiboev I., “On some eigenvalue problems for an equation of mixed type, ” in: The International Conference “Partial Differential Equations and Related Problems of Analysis and Informatics,” 2004, Vol. 1, pp. 285–286.
Urinov A. K., “Some eigenvalue problems for a mixed-type equation with singular coefficient, ” Uzbek. Mat. Zh., No. 1, 70–78 (2005).
Kapilevich M. B., “On one class of Horn’s hypergeometric functions,” Differentsial’nye Uravneniya, 4, No. 8, 1466–1483 (1968).
Bateman H. and Erdélyi A., Higher Transcendental Functions. Vol. 1 [Russian translation], Nauka, Moscow (1965).
Samko S. G., Kilbas A. A., and Marichev O. M., Integrals and Fractional-Order Derivatives and Some of Their Applications [in Russian], Nauka i Tekhnika, Minsk (1987).
Gradshtein I. S. and Ryzhik I. M., Tables of Integrals, Sums, Series, and Products [in Russian], Nauka, Moscow (1962).
Kuznetsov D. S., Special Functions [in Russian], Vysshaya Shkola, Moscow (1965).
Gordeev A. M., “Some boundary-value problems for a generalized Euler-Poisson-Darboux equation, ” Volzhskiĭ Mat. Sb., No. 6, 56–61 (1968).
Salakhitdinov M. S. and Islomov B., “Some Boundary-Value Problems with Displacement for the Equation-(−y)m u xx + x n u yy − λ2 x n(−y)m u = 0,” in: Nonclassical Equations in Mathematical Physics and Problems of Branching Theory [in Russian], Fan, Tashkent, 1988, pp. 24–34.
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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 48, No. 4, pp. 882–893, July–August, 2007.
Original Russian Text Copyright © 2007 Salakhitdinov M. S. and Urinov A. K.
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Salakhitdinov, M.S., Urinov, A.K. Eigenvalue problems for a mixed-type equation with two singular coefficients. Sib Math J 48, 707–717 (2007). https://doi.org/10.1007/s11202-007-0072-7
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DOI: https://doi.org/10.1007/s11202-007-0072-7