Geodesic
On stability of perturbed semigroups in partially ordered Banach spaces
Contemporary Mathematics. Fundamental Directions, Proceedings of the Seventh International Conference on Differential and Functional-Differential Equations (Moscow, August 22–29, 2014). Part 2, Tome 59 (2016), pp. 97-118

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We prove necessary and sufficient conditions for stability of perturbed semigroups of linear operators in Banach spaces with cones and consider some examples of using these conditions. In particular, we consider an example where the boundary-value problem is perturbed by a linear operator with delayed argument and establish conditions of stability for such a perturbed semigroup. 
@article{CMFD_2016_59_a4,
     author = {M. I. Kamenskii and I. M. Gudoshnikov},
     title = {On stability of perturbed semigroups in partially ordered {Banach} spaces},
     journal = {Contemporary Mathematics. Fundamental Directions},
     pages = {97--118},
     publisher = {mathdoc},
     volume = {59},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2016_59_a4/}
}
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M. I. Kamenskii; I. M. Gudoshnikov. On stability of perturbed semigroups in partially ordered Banach spaces. Contemporary Mathematics. Fundamental Directions, Proceedings of the Seventh International Conference on Differential and Functional-Differential Equations (Moscow, August 22–29, 2014). Part 2, Tome 59 (2016), pp. 97-118. http://geodesic.mathdoc.fr/item/CMFD_2016_59_a4/