Geodesic
On one non-local problem for axisymmetric Helmholtz equation
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 3 (2011), pp. 26-34

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Non-local boundary problem for the axisymmetric Helmholtz equation is explored. The uniqueness of the solution is proved by the spectral method. The conditions of solvability are found. The solution of the problem is constructed in the form of the biorthogonal series.
Keywords: Helmholtz equation, Bessel functions, non-local boundary problem, Riesz basis. 
@article{VSGTU_2011_3_a1,
     author = {A. A. Abashkin},
     title = {On one non-local problem for axisymmetric {Helmholtz} equation},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
     pages = {26--34},
     publisher = {mathdoc},
     number = {3},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGTU_2011_3_a1/}
}
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A. A. Abashkin. On one non-local problem for axisymmetric Helmholtz equation. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 3 (2011), pp. 26-34. http://geodesic.mathdoc.fr/item/VSGTU_2011_3_a1/