Marynets K. Investigation of solutions of the non-linear boundary-value problems with parametrization.

This work is devoted to some new approach of parametrization for transformation of boundary-value problems with nonlinear two-point and multi-point, non-separated boundary conditions with singular matrixes and restrictions with integral terms to the two-point ones with linear conditions satisfying some determining systems. For investigation of the parametrized problems there were built the numerical-analytic schemes with improved characteristics of convergence. We prove the control parameter theorems, establish necessary and sufficient conditions of solvability. The theoretical results were detailed illustrated on applications.