We explore the Hyers–Ulam stability of perturbations for a homogeneous linear differential system with $$2\times 2$$ constant coefficient matrix. New necessary and sufficient conditions to be stable are proven, first time, best (minimal) systems is found in some cases. Several examples provided. Obtaining second-order equations illustrates applicability strong results.

Spherically symmetric thin-shell wormholes in the presence of a cosmological constant are constructed applying the cut-and-paste technique implemented by Visser. Using the Darmois-Israel formalism the surface stresses, which are concentrated at the wormhole throat, are determined. This construction allows one to apply a dynamical analysis to the throat, considering linearized radial perturbatio...