Ukr. Mat. Zh. - 2018. - 70, № 1. - pp. 94-114
We show how an appropriate parametrization technique and successive approximations can help to investigate nonlinear boundary-value problems for systems of differential equations under the condition that the components of solutions vanish at some unknown points. The technique can be applied to nonlinearities involving the signs of absolute value and positive or negative parts of functions under various types of boundary conditions.