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 $R_2^{+}=\left\{\left(x,y\right):x>0,y>0\right\}.$ 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.

11 pages