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Gewöhnliche lineare Differentialgleichungen n−ter Ordnung mit Distributionskoeffizienten

Published online by Cambridge University Press:  14 November 2011

Rainer Pfaff
Rainer Pfaff
Affiliation:
Fachbereich Mathematik, Technische Hochschule Darmstadt, West Germany
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Synopsis

We 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.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 85 , Issue 3-4 , 1980 , pp. 291 - 298
Copyright
Copyright © Royal Society of Edinburgh 1980

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References

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