On a nonlinear boundary value problems with impulse action

Abstract

In this work, a boundary value problems for a system of nonlinear ordinary differential equations that incorporates impulsive actions is considered. This formulation is significant for modeling real-world phenomena in which abrupt changes occur at specific time instants. The study established sufficient conditions for the existence of isolated solutions to the proposed boundary value problems. This is crucial to ensure that the mathematical models accurately reflect the behavior of systems subject to impulsive actions. Algorithms were developed to find solutions to the boundary value problems. These algorithms leverage the parameterization method, which is effective in handling the discontinuities introduced by impulsive actions. The research includes a numerical implementation of the proposed algorithms, demonstrating their practicality and effectiveness in solving the boundary value problems with impulsive actions. The findings have implications in various fields, including mechanics, electrical engineering, and biology, where systems often experience sudden changes due to external influences. In general, the research contributes to the understanding and solution of nonlinear boundary value problems affected by impulsive actions, providing a framework for further exploration and application in scientific and engineering contexts.