Application of the Parameterization Method to Nonlinear Boundary Value Problem With a Nonfixed Moment of Impulsive Action

ABSTRACT This paper investigates a nonlinear boundary value problem for a system of linear differential equations with a nonfixed moment of impulsive action. To address this problem, we apply the Dzhumabaev parameterization method, which is adapted to account for the nonlinearity of the boundary conditions and the presence of an unknown impulsive moment. These features required modifications of the classical schemes of the method, leading to the development of new algorithms that incorporate the non‐fixed impulsive action. The main contribution of this work is the extension of the applicability of the parameterization method and the derivation of solvability conditions for the problem under consideration. To illustrate the theoretical results, an example is presented.