Periodic problem for an impulsive system of the loaded hyperbolic equations

We consider a periodic problem for a system of the loaded hyperbolic equations with impulse effects. By introducing additional functions, this problem is reduced to an equivalent problem consisting of a family of periodic boundary-value problems of loaded ordinary differential equations with impulse effects and integral relations. We obtain sufficient conditions for the existence of unique solution to the family of periodic boundary-value problems. Conditions of unique solvability of periodic problem are established in terms of initial data