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Generalized systems of linear differential equations

Published online by Cambridge University Press:  14 November 2011

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

Synopsis

We consider ordinary linear differential systems of first order with distributional coefficients and distributional nonhomogeneous terms. Firstly the coefficients are assumed to be functions, secondly to be first order distributions (i.e. first derivatives of functions which are integrable or of bounded variation), and thirdly to be distributions of higher order.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 1981

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References

1Antosik, P., Mikusinski, J. and Sikorski, R.. Theory of distributions. The sequential approach (Amsterdam: Elsevier; Warszawa: PWN, 1973).Google Scholar
2Antosik, P. and Ligeza, J.. Products of measures and functions of finite variations. Proceedings of the conference on generalized functions and operational calculus, Varna 1975, p. 2026 (Sofia: Bulgarian Academy of Sciences, 1979).Google Scholar
3Jantscher, L.. Distributionen (Berlin, New York: de Gruyter, 1971).CrossRefGoogle Scholar
4Kurzweil, J.. Linear differential equations with distributions as coefficients. Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 7 (1959), 557560.Google Scholar
5Lasota, A.. Remarks on linear differential equations with distributional perturbations. Ordinary differential equations (Proc. NRL-MRC Conf., Math. Res. Center, Naval Res. Lab., Washington, D.C., 1971), p. 489495 (New York: Academic Press, 1972).CrossRefGoogle Scholar
6Ligeza, J.. On generalized solutions of linear differential equations of order n. Uniw. Ślaski w Katowicach-Prace Mat. 3 (1973), 101108.Google Scholar
7Ligeza, J.. On distributional solutions of some systems of linear differential equations. Časopis Pěst. Mat. 102 (1977), 3741.CrossRefGoogle Scholar
8Pfaff, R.. Zur Theorie der gewöhnlichen linearen Differentialgleichung zweiter Ordnung mit Distributionskoeffizient (Technische Hochschule Darmstadt. Dissertation, 1978). University Microfilms International no. 79–70, 022.Google Scholar
9Pfaff, R.. Gewöhnliche lineare Differentialgleichungen zweiter Ordnung mit Distributionskoeffizient. Arch. Math. (Basel) 32 (1979), 469478.CrossRefGoogle Scholar
10Pfaff, R.. Gewöhnliche lineare Differentialgleichungen n-ter Ordnung mit Distributions koeffizienten. Proc. Roy. Soc. Edinburgh Sect. A 85 (1980), 291298.CrossRefGoogle Scholar
11Schwabik, Š.. Verallgemeinerte lineare Differentialgleichungssysteme. Časopis Pěst. Mat. 96 (1971), 183211.CrossRefGoogle Scholar
12Schwabik, Š., Tvrdý, M. and Vejvoda, O.. Differential and Integral equations (Dordrecht: Reidel Publishing Co. 1979).Google Scholar
13Walter, W.. Einführung in die Theorie der Distributionen (Mannheim/Wien/Zürich: Bibliographisches Institut, 1974).Google Scholar