Within the Oseen-Frank theory we derive numerically exact solutions for axisymmetric localized states in chiral liquid crystal layers with homeotropic anchoring. These solutions describe recently observed two-dimensional skyrmions in confinement-frus
trated chiral nematics [P. J. Acherman et al. Phys. Rev. E 90, 012505 (2014)]. We stress that these solitonic states arise due to a fundamental stabilization mechanism responsible for the formation of skyrmions in cubic helimagnets and other noncentrosymmetric condensed-matter systems.
In cubic noncentrosymmetric ferromagnets uniaxial distortions suppress the helical states and stabilize Skyrmion lattices in a broad range of thermodynamical parameters. Using a phenomenological theory for modulated and localized states in chiral mag
nets, the equilibrium parameters of the Skyrmion and helical states are derived as functions of the applied magnetic field and induced uniaxial anisotropy. These results show that due to a combined effect of induced uniaxial anisotropy and an applied magnetic field Skyrmion lattices can be formed as thermodynamically stable states in large intervals of magnetic field and temperatures in cubic helimagnets, e.g., in intermetallic compounds MnSi, FeGe, (Fe,Co)Si. We argue that this mechanism is responsible for the formation of Skyrmion states recently observed in thin layers of Fe_{0.5}Co_{0.5}Si [X.Z.Yu et al., Nature textbf{465}(2010) 901].
