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Limit-point criteria for systems of differential equations

Published online by Cambridge University Press:  14 November 2011

Hilbert Frentzen
Hilbert Frentzen
Affiliation:
Department of Mathematics, University of Essen, Germany
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Synopsis

For a certain class of first order systems of differential equations several theorems are derived which give sufficient conditions for an appropriate sesquilinear form to be identically zero on suitable spaces of solutions of the system. As a consequence for second order systems limit-point criteria are obtained which include rather general criteria in the case of second order equations. The method used involves sequences of auxiliary functions and is most expedient for the proof of interval limit-point criteria. The theory is also applicable to second order equations with complex coefficients yielding sufficient conditions for the existence of solutions which are not of integrable square.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 85 , Issue 3-4 , 1980 , pp. 233 - 245
Copyright
Copyright © Royal Society of Edinburgh 1980

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