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Mild solutions of second-order differential equations on the line

Published online by Cambridge University Press:  01 July 2000

SIBYLLE SCHWEIKER
Affiliation:
Abteilung Mathematik V, Universität Ulm, 89069 Ulm, Germany; e-mail: sibylle@mathematik.uni-ulm.de

Abstract

A necessary condition for the existence and uniqueness of mild solutions of first- and second-order differential equations on the real line is given. It is known that the first-order problem is related to the operator equation AXXD = −δ0. Here, it is shown how the second-order problem on the real line is connected to the operator equation AXXD2 = −δ0 and also to some other operator equations.

Type
Research Article
Copyright
2000 Cambridge Philosophical Society

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