Continuous dependence of the solutions of impulsive differential equations on the initial conditions and barrier curves

Abstract

The basic objects of investigation in this article are nonlinear impulsive differential equations. The impulsive moments coincide with the moments of meeting of the integral curve and some of the so-called barrier curves. For such type of equations, sufficient conditions are found under which the solutions are continuously dependent on the perturbations with respect to the initial conditions and barrier curves. The results are applied to a mathematical model of population dynamics.