The stability of certain retarded systems with variable coefficients (Q1359921)

The proposed extension of the Krasovsky method is based on the frequently used artifice of transforming `troublesome' terms into `higher order perturbations'. Subject to certain conditions the latter become `small' compared to the dominant parts. Several of these conditions are tacit and constitute restrictions. It was already known to \textit{E. Schmidt} [Math. Ann. 70, 499-524 (1911; JFM 42.0351.01)] that in addition to the coefficient \(b\) and the nominal delay \(h\), the product \(bh\) must be also considered. -- In the paper an inverse function \(q(t)\) is used. This \(q(t)\) is not necessarily unique and single-valued, and may even not exist (Bessel functions have no `ordinary' inverses). It is thus advisable to use the proposed extension with great caution.