Gewöhnliche lineare Differentialgleichungen n−ter Ordnung mit Distributionskoeffizienten

SynopsisWe give a formula (4) for a variety of ordinary linear differential equations of order n with distributional coefficients. There appear as coefficients distributions of order k ≦ n/2, i.e. these distributions are kth distributional derivatives of locally L-integrable functions. With a suitable transformation (7) the differential equations can be transformed into first order systems (8) with integrable coefficients. From this follows the existence of a continuous solution, which can be uniquely determined by proper initial conditions.The coefficients in the differential equations considered are chosen as general as possible but such that a transformation into a system with integrable coefficients can be performed, and that all products are defined by Leibniz' formula.