The Dirichlet problem for the generalized bi-axially symmetric Helmholtz equation

Abstract

In [18], fundamental solutions for the generalized bi-axially symmetric Helmholtz equation were constructed in \( \mathbb{R}^+_2 = \{ (x, y) : x > 0, y > 0 \} \). 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 \( \Omega \subset \mathbb{R}^+_2 \). Using the method of Green’s functions, solution of this problem is found in an explicit form.