Well-Posed Solvability of a Nonlocal Boundary-Value Problem for the Systems of Hyperbolic Equations with Impulsive Effects

Abstract

We consider a nonlocal boundary-value problem for a system of hyperbolic equations with impulsive effects. The relationship is established between the well-posed solvability of the nonlocal boundary-value problem for a system of hyperbolic equations with impulsive effects and the well-posed solvability of a family of two-point boundary-value problems for a system of ordinary differential equations with impulsive effects. Sufficient conditions for the existence of a unique solution of the family of two-point boundary-value problems for a system of ordinary differential equations with impulsive effects are obtained by method of introduction of functional parameters. The algorithms are proposed for finding the solutions. The necessary and sufficient conditions of the well-posed solvability of a nonlocal boundary-value problem for a system of hyperbolic equations with impulsive effects are established in the terms of the initial data.