On parametrization for a non-linear boundary value problem with separated conditions

M. Ronto, University of Miskolc, Miskolc-Egyetemváros, Hungary
N. Shchobak, Mathematical Faculty, Uzhgorod National University, Ukraine

E. J. Qualitative Theory of Diff. Equ., Proc. 8'th Coll. Qualitative Theory of Diff. Equ., No. 18. (2008), pp. 1-16.

Abstract: We obtain some results concerning the investigation of two-dimensional non-linear boundary value problems with two-point separated linear boundary conditions.
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. The parametrized problem should be investigated together with certain so-called determining equations, which have algebraic or transcendental form.

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