On Stability of Perturbed Semigroups in Partially Ordered Banach Spaces

We prove necessary and sufficient stability conditions for perturbed semigroups of linear operators in Banach spaces with cones and consider examples using these conditions. In particular, we consider an example where the boundary-value problem is perturbed by a linear operator with a delayed independent variable and establish stability conditions for such a perturbed semigroup. © 2018, Springer Science+Business Media, LLC, part of Springer Nature.