On the unique solvability of a nonlocal boundary-value problem for systems of loaded hyperbolic equations with impulsive actions

Abstract

We consider a nonlocal boundary-value problem with impulsive actions for a system of loaded hyperbolic equations and establish the relationship between the unique solvability of this problem and the unique solvability of a family of two-point boundary-value problems with impulse actions for the system of the loaded ordinary differential equations by method of introduction of additional functions. Sufficient conditions are obtained for the existence of a unique solution to a family two-point boundary-value problems with impulsive effects for the system of loaded ordinary differential equations by using method of parametrization. The algorithms of finding the solutions are constructed. The conditions of unique solvability of the nonlocal boundary-value problem for a system of loaded hyperbolic equations with impulsive actions are established. The numerical realization of the algorithms of the method of parametrization is proposed for the solution of the family of two-point boundary-value problems with impulsive actions for the system of the loaded ordinary differential equations. The results are illustrated by specific examples.