Abstract:
In the article, the second homogeneous boundary value problem is considered in an infinite angular domain.
Solution of the problem is reduced to solving the singular Volterra integral equations of the second kind with
kernel whose norm is equal to unity. By the method of Carleman-Vekua, solving the integral equation is reduced
to solving the inhomogeneous equation of Abel. The theorem on the existence of a non-trivial solution
of the second homogeneous boundary value problem in a non-cylindrical domain is proved. The solution of
the given problem is obtained in an explicit form.
