The Dirichlet problem for the generalized bi-axially symmetric Helmholtz equation - Salakhitdinov, Makhmud Salakhitdinovich; Hasanov, Anvar (Eurasian Mathematical Journal, 2012)
In [18], fundamental solutions for the generalized bi-axially symmetric Helmholtz equation were constructed in \( R^+_2 = { (x, y) : x > 0, y > 0 } \). 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 \( Ω R^+_2 \). Using the method of Green’s functions, solution of this problem is found in an explicit form.