Nonlinear matrix differential-algebraic boundary value problem

Abstract

We set forth solvability conditions and construction of the generalized Green’s operator for Noetherian boundary value problem for the matrix differential-algebraic equations and solvability conditions and the constructive scheme for constructing solutions of nonlinearNoetherian boundary value problem for matrix differential-algebraic equation. We show that the principal results in the theory of weakly nonlinear periodic oscillations remain valid for nonlinear Noetherian boundary value problem for matrix differential-algebraic equation. The study is illustrated by the periodic problem for a Duffing-type matrix differential equation.