Geodesic
On stabilization of solutions of singular elliptic equations
Fundamentalʹnaâ i prikladnaâ matematika, Tome 12 (2006) no. 4, pp. 169-186

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Linear and quasi-linear elliptic equations containing the Bessel operator with respect to a selected variable (so-called special variable) are studied. The well-posedness of the nonclassical Dirichlet problem (with the additional condition of evenness with respect to the special variable) in the half-space is proved, an integral representation of the solution is constructed, and a necessary and sufficient condition of the stabilization is established. The stabilization is understood as follows: the solution has a finite limit as the independent variable tends to infinity along the direction orthogonal to the boundary hyperplane. 
@article{FPM_2006_12_4_a10,
     author = {A. B. Muravnik},
     title = {On stabilization of solutions of singular elliptic equations},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {169--186},
     publisher = {mathdoc},
     volume = {12},
     number = {4},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2006_12_4_a10/}
}
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A. B. Muravnik. On stabilization of solutions of singular elliptic equations. Fundamentalʹnaâ i prikladnaâ matematika, Tome 12 (2006) no. 4, pp. 169-186. http://geodesic.mathdoc.fr/item/FPM_2006_12_4_a10/