On the parametrization of boundary-value problems with two-point nonlinear boundary conditions

Abstract

We obtain some results for the solutions of nonlinear boundary-value problems of a certain type with two-point nonlinear boundary conditions and reveal the efficiency of the procedure of reduction of the analyzed problem to a parametrized boundary-value problem with linear boundary conditions containing certain artificially introduced parameters. To study the transformed two-point problem, we propose a method based on the approximations of a special type constructed in the analytic form. It is shown that these approximations uniformly converge to a parametrized limit function and establish the relationship between this function and the exact solution. The proposed procedure leads to a certain system of algebraic equations whose solutions give numerical values of the parameters corresponding to the solution of the given two-point nonlinear boundary-value problem.