Distributional derivatives of functions of two variables of finite variation and their application to an impulsive hyperbolic equation

We give characterizations of the distributional derivatives D ^1,1, D ^1,0, D ^0,1 of functions of two variables of locally finite variation. Then we use these results to prove the existence theorem for the hyperbolic equation with a nonhomogeneous term containing the distributional derivative determined by an additive function of an interval of finite variation. An application of the above theorem to a hyperbolic equation with an impulse effect is also given.