Iterative method for solving a non-linear edge problems with a point source

In this paper, we consider the first boundary value problem for a quasilinear equation in a bounded domain with a point source. The solution of the problem is sought in the form of the sum of three functions. The first function is represented explicitly and is the solution of a linear equation with a point source with constant coefficients. The second function is found from the solution of a linear homogeneous boundary value problem with constant coefficients. To search for the third function an iterative process is used that converges strongly in the Sobolev space at the rate of a geometric progression.