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.
© 2012 Miklós Rontó, Natalia Shchobak, published by Slovak Academy of Sciences, Mathematical Institute
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