Displaying similar documents to “The existence and the uniqueness of distributional solutions of some systems of non-linear differential equations”

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

Dariusz Idczak (1998)

Czechoslovak Mathematical Journal

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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.