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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Ordinary differential inequalities
and quasimonotonicity
in ordered topological vector spaces


Author: Roland Uhl
Journal: Proc. Amer. Math. Soc. 126 (1998), 1999-2003
MSC (1991): Primary 34G20, 34A40, 47H07
MathSciNet review: 1443412
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Abstract: A well known comparison theorem on ordinary differential inequalities with quasimonotone right-hand side $f(t,x)$ was carried over by
Volkmann (1972) to (pre)ordered topological vector spaces. We prove that the quasimonotonicity of $f$ is a necessary condition here if $f$ is continuous. Then it is shown that quasimonotonicity can be verified by considering only a few positive continuous linear functionals in the definition (for instance in $\ell _{\infty}$ by taking coordinate functionals).


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Additional Information

Roland Uhl
Affiliation: Mathematisches Institut II, Universität Karlsruhe, D-76128 Karlsruhe, Germany
Email: roland.uhl@math.uni-karlsruhe.de

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04311-1
PII: S 0002-9939(98)04311-1
Keywords: Quasimonotonicity, ordinary differential inequalities, comparison or monotonicity theorems, lower and upper solutions, ordered topological vector spaces
Received by editor(s): December 10, 1996
Communicated by: Hal L. Smith
Article copyright: © Copyright 1998 American Mathematical Society