Parametrizaion for some boundary value problems of interpolation type

Abstract

We obtain some results concerning the investigation of two-dimensional
non-linear boundary value problems of interpolation type. We show that it is useful to reduce the given boundary value problem, using
an appropriate substitution, to a parametrized boundary value problem
containing some unknown scalar parameter in the boundary conditions.
To study the transformed parametrized problem,  we use a
method which is based upon special types of successive approximations constructed in an
analytic form.