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Ordinary differential inequalities and quasimonotonicity in ordered topological vector spaces |
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| Authors: | Roland Uhl |
| Institution: | Mathematisches Institut II, Universität Karlsruhe, D-76128 Karlsruhe, Germany |
| Abstract: | A well known comparison theorem on ordinary differential inequalities with quasimonotone right-hand side  was carried over by Volkmann (1972) to (pre)ordered topological vector spaces. We prove that the quasimonotonicity of  is a necessary condition here if  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  by taking coordinate functionals). |
| Keywords: | Quasimonotonicity ordinary differential inequalities comparison or monotonicity theorems lower and upper solutions ordered topological vector spaces |
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