Geodesic
The Dirichlet problem for the generalized bi-axially symmetric Helmholtz equation
Eurasian mathematical journal, Tome 3 (2012) no. 4, pp. 99-110

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In [18], fundamental solutions for the generalized bi-axially symmetric Helmholtz equation were constructed in $R^+_2=\{(x,y)\colon x>0,\ y>0\}$. They contain Kummer's confluent hypergeometric functions in three variables. In this paper, using one of the constructed fundamental solutions, the Dirichlet problem is solved in the domain $\Omega\subset R^+_2$. Using the method of Green's functions, solution of this problem is found in an explicit form. 
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     author = {M. S. Salakhitdinov and A. Hasanov},
     title = {The {Dirichlet} problem for the generalized bi-axially symmetric {Helmholtz} equation},
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M. S. Salakhitdinov; A. Hasanov. The Dirichlet problem for the generalized bi-axially symmetric Helmholtz equation. Eurasian mathematical journal, Tome 3 (2012) no. 4, pp. 99-110. http://geodesic.mathdoc.fr/item/EMJ_2012_3_4_a7/