Geodesic
On a weighted boundary value problem in an infinite half-strip for a biaxisymmetric Helmholtz equation
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2013), pp. 3-12
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We study a boundary value problem for a generalized biaxisymmetric Helmholtz equation. Boundary conditions in this problem depend on equation parameters. By the variable separation method, using the Fourier–Bessel series expansion and the Hankel transform, we prove the unique solvability of the problem and establish explicit formulas for the solution.
Keywords: Helmholz equation, Fourier–Bessel series, Hankel transformation, Bessel functions. 
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     author = {A. A. Abashkin},
     title = {On a~weighted boundary value problem in an infinite half-strip for a~biaxisymmetric {Helmholtz} equation},
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A. A. Abashkin. On a weighted boundary value problem in an infinite half-strip for a biaxisymmetric Helmholtz equation. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2013), pp. 3-12. http://geodesic.mathdoc.fr/item/IVM_2013_6_a0/

[1] Marichev O. I., Kilbas A. A., Repin O. A., Kraevye zadachi dlya uravnenii v chastnykh proizvodnykh s razryvnymi koeffitsientami, Izd-vo SGEU, Samara, 2008 | Zbl

[2] Lerner M. E., Repin O. A., “O zadache Dirikhle dlya obobschennogo dvuosesimmetricheskogo uravneniya Gelmgoltsa v pervom kvadrante”, Vestn. Samarsk. tekhnicheskogo un-ta, 6, 1998, 5–8

[3] Lerner M. E., Repin O. A., “Nelokalnye kraevye zadachi v vertikalnoi polupolose dlya obobschennogo osesimmetricheskogo uravneniya Gelmgoltsa”, Differents. uravneniya, 37 (2001), 1562–1564 | MR | Zbl

[4] Moiseev E. I., “O razreshimosti odnoi nelokalnoi kraevoi zadachi”, Differents. uravneniya, 37 (2001), 1565–1567 | MR | Zbl

[5] Shimkovich E. V., “O vesovykh kraevykh zadachakh dlya vyrozhdayuschegosya uravneniya ellipticheskogo tipa v polupolose”, Litovsk. matem. sb., 30 (1990), 185–196 | MR | Zbl

[6] Ruziev M. Kh., “Zadacha Dirikhle v vertikalnoi polupolose dlya vyrozhdayuschegosya ellipticheskogo uravneniya s singulyarnym koeffitsientom i so spektralnym parametrom”, Materialy konf. “Differentsialnye uravneniya, teoriya funktsii i prilozheniya”, Novosibirsk, 2007, 268–269

[7] Lebedev N. N., Spetsialnye funktsii i ikh prilozheniya, Lan, SPb., 2010