Nonlinear boundary-value problems for systems of ordinary differential equations - Boichuk О. A. (Ukrains’kyi Matematychnyi Zhurnal, 1998)
We consider nonlinear boundary-value problems (with Noetherian operator in the linear part) for systems of ordinary differential equations in the neighborhood of generating solutions. By using the Lyapunov — Schmidt method, we establish conditions for the existence of solutions of these boundary-value problems and propose iteration algorithms for their construction.