FWeakly Nonlinear Boundary-Value Problems for Systems of Impulsive Integrodifferential Equations. Critical Case of the Second Order

Abstract

We establish conditions for the existence of solutions of an impulsive weakly nonlinear boundary-value problem in the critical case of the second order and determine the structure of these solutions. By using the theory of orthoprojectors and pseudoinverse Moore–Penrose matrices, we study sufficient conditions for the existence of solutions of problems of this kind and propose an iterative algorithm for their construction. It is shown that the existence of solution of the original boundary-value problem depends on the conditions obtained with regard for nonlinearity and the second approximation to the required solution. It is proposed to consider the impulsive problem as an inner boundary-value problem.