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May 2008 Comparison Results for Generalized Kolmogorov Systems with Respect to Multiplicative Semigroups
Gerd Herzog, Roland Lemmert
Missouri J. Math. Sci. 20(2): 115-126 (May 2008). DOI: 10.35834/mjms/1316032812

Abstract

The group $G(\mathcal{A})$ of the invertible elements of a Banach algebra $\mathcal{A}$ can be pre-ordered by a closed semigroup $S$. We prove a comparison theorem for ODEs of the form $u'=f_1(t,u) u + u f_2(t,u)$ in Banach algebras under the assumption that $S$ is permutation stable. Applications to monotonicity properties of initial value problems and dynamical systems are given.

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Gerd Herzog. Roland Lemmert. "Comparison Results for Generalized Kolmogorov Systems with Respect to Multiplicative Semigroups." Missouri J. Math. Sci. 20 (2) 115 - 126, May 2008. https://doi.org/10.35834/mjms/1316032812

Information

Published: May 2008
First available in Project Euclid: 14 September 2011

zbMATH: 1154.34028
Digital Object Identifier: 10.35834/mjms/1316032812

Subjects:
Primary: 34C11
Secondary: 34C12 , 34G20

Rights: Copyright © 2008 Central Missouri State University, Department of Mathematics and Computer Science

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Vol.20 • No. 2 • May 2008
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