Geodesic
On one problem in an infinity half-strip for~biaxisimmetric Helmholtz equation
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 1 (2012), pp. 39-45.

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Boundary value problem in an infinity half-strip for biaxisymmetric Helmholtz equation is explored. Existence conditions of this problem are gotten with help of Fourier–Bessel series expansion. Uniqueness of solution of this boundary value problem is proved for some parameters values. Lack of uniqueness of solution is proved for some other parameters values.
Mots-clés : Helmholtz equation, boundary value problem, Fourier–Bessel series, Bessel functions, maximum principle. 
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A. A. Abashkin. On one problem in an infinity half-strip for~biaxisimmetric Helmholtz equation. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 1 (2012), pp. 39-45. https://geodesic-test.mathdoc.fr/item/VSGTU_2012_1_a3/

[1] Moiseev E. I., “Solvability of a nonlocal boundary value problem”, Differ. Equ., 37:11 (2001), 1643–1646 | DOI | MR | Zbl

[2] Lerner M. E., Repin O. A., “Nonlocal boundary value problems in a vertical half-strip for a generalized axisymmetric Helmholtz equation”, Differ. Equ., 37:11 (2001), 1640–1642 | DOI | MR | Zbl

[3] Lebedev N. N., Special Functions and Their Applications, Lan', St. Petersburg, 2010, 368 pp.

[4] Olver F., Asymptotics and special functions, Nauka, Moscow, 1990, 528 pp. | MR | Zbl