Geodesic
On a problem for a three-dimensional elliptic equation with Bessel operators
Čelâbinskij fiziko-matematičeskij žurnal, Tome 9 (2024) no. 3, pp. 375-388

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The Keldysh problem for a three-dimensional elliptic equation with three singular coefficients in a rectangular parallelepiped is studied. Based on the property of completeness of systems of eigenfunctions of two one-dimensional spectral problems, a uniqueness theorem is proved. The solution to the problem posed is constructed as the sum of a double Fourier — Bessel series.
Keywords: Keldysh problem, elliptic equation, spectral method, singular coefficient, Bessel function. 
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     author = {K. T. Karimov},
     title = {On a problem for a three-dimensional elliptic equation with {Bessel} operators},
     journal = {\v{C}el\^abinskij fiziko-matemati\v{c}eskij \v{z}urnal},
     pages = {375--388},
     publisher = {mathdoc},
     volume = {9},
     number = {3},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHFMJ_2024_9_3_a2/}
}
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K. T. Karimov. On a problem for a three-dimensional elliptic equation with Bessel operators. Čelâbinskij fiziko-matematičeskij žurnal, Tome 9 (2024) no. 3, pp. 375-388. http://geodesic.mathdoc.fr/item/CHFMJ_2024_9_3_a2/