On Solutions of Nonlinear Boundary-Value Problems Whose Components Vanish at Certain Points

Abstract

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 certain unknown points. The technique can be applied to nonlinearities involving the signs of the absolute value and positive or negative parts of functions under boundary conditions of various types.