Comparison results for generalized Kolmogorov systems with respect to multiplicative semigroups (Q932404)

The paper deals with comparison problems for ODEs of the form \[ u'=f_1(t,u)u+uf_2(t,u) \] in the group \({\mathcal{G(A)}}\) of all invertible elements of a Banach algebra \({\mathcal{A}}.\) The order in the space is defined by a closed semigroup \(S\) which is permutation stable. Some applications of the general results are given on initial value problems and dynamical systems, while some examples illustrate the results.