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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Über gewöhnliche Differentialungleichungen zweiter Ordnung


Author: Roland Lemmert
Journal: Proc. Amer. Math. Soc. 83 (1981), 720-724
MSC: Primary 34A30
DOI: https://doi.org/10.1090/S0002-9939-1981-0630027-4
MathSciNet review: 630027
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Abstract: A theorem about the separation of sub- and superfunctions $ \upsilon $ and $ w$ by solutions of an ordinary differential equation of second order is proved, where $ \upsilon \geqslant w$ throughout the given interval. Examples show that the condition imposed on the right side $ f$ of the equation is sharp, and that an analogous theorem is not true for Laplace's equation, even in the case $ f \equiv 0,\upsilon $ sub- and $ w$ superharmonic.


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DOI: https://doi.org/10.1090/S0002-9939-1981-0630027-4
Keywords: Generalized convex functions, separation theorem
Article copyright: © Copyright 1981 American Mathematical Society