We determine eigenvalues and eigenfunctions of the Gellerstedt problem for the multidimensional Lavrent’ev–Bitsadze equation.
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References
E. I. Moiseev, Equations of Mixed Type with Spectral Parameter [in Russian], Moscow University, Moscow (1988).
T. Sh. Kal’menov, On Regular Boundary-Value Problems and Their Spectrum for Equations of Hyperbolic and Mixed Types [in Russian], Author’s Abstract of the Doctoral-Degree Thesis (Physics and Mathematics), Moscow (1982).
S. M. Ponomarev, “On the eigenvalue problem for the Lavrent’ev–Bitsadze equation,” Dokl. Akad. Nauk SSSR, 223, 39–40 (1977).
M. S. Salakhitdinov and A. K. Urinov, Boundary-Value Problems for Equations of Mixed Type with Spectral Parameter [in Russian], Fan, Tashkent (1977).
K. B. Sabitov, “On the Tricomi problem for the Lavrent’ev–Bitsadze equation with spectral parameter,” Differents. Uravn., 22, No. 11, 1977–1984 (1986).
A. M. Nakhushev, Problems with Displacement for Partial Differential Equations [in Russian], Nauka, Moscow (2006).
S. G. Mikhlin, Multidimensional Singular Integrals and Integral Equations [in Russian], Fizmatgiz, Moscow (1962).
E. Kamke, Differentialgleichungen Lösungsmethoden und Lösungen, Akademische Verlagsgesellschaft Geest, Leipzig (1959).
H. Bateman and A. Erdélyi, Higher Transcendental Functions, Vol. 2, McGraw-Hill, New York (1954).
H. Bateman and A. Erdélyi, Higher Transcendental Functions, Vol. 1, McGraw-Hill, New York (1954).
S. A. Aldashev, Degenerating Multidimensional Hyperbolic Equations [in Russian], ZKATU, Oral (2007).
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 63, No. 6, pp. 827–832, June, 2011.
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Aldashev, S.A. Eigenvalues and eigenfunctions of the Gellerstedt problem for the multidimensional Lavrent’ev–Bitsadze equation. Ukr Math J 63, 962–968 (2011). https://doi.org/10.1007/s11253-011-0555-3
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DOI: https://doi.org/10.1007/s11253-011-0555-3