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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
SIBYLLE SCHWEIKER
Affiliation:
Abteilung Mathematik V, Universität Ulm, 89069 Ulm, Germany; e-mail: sibylle@mathematik.uni-ulm.de
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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 AX − XD = −δ0. Here, it is shown how the second-order problem on the real line is connected to the operator equation AX − XD2 = −δ0 and also to some other operator equations.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 129 , Issue 1 , July 2000 , pp. 129 - 151
Copyright
2000 Cambridge Philosophical Society

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