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.
Citation
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
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