Stability in delay perturbed differential and difference equations (Q2738681)

Let \(u(t;\tau)\) be the fundamental solution to the linear delay differential equation \(\dot x(t) = - x(t-\tau)\), \(t\geq 0\) and set \(\Phi(\tau) := \int_{0}^{\infty} |u(t;\tau)|dt\). After summarizing the authors' earlier work, several new stability results (i.e. preserving the stability under delay perturbation) on linear differential and difference equations are formulated with the help of the function \(\Phi\). In order to apply the results, the authors derive upper estimates on \(\Phi\). It is shown that these results improve many known so-called \(3/2\)-type or \(\pi/2\)-type stability theorems. Some open problems are presented.NEWLINENEWLINEFor the entire collection see [Zbl 0960.00044].