  We study a frustrated antiferromagnetic Heisenberg model on a triangular
lattice with the Dzyaloshinskii-Moriya interaction (DMI) in the presence of an
external magnetic field and a single-ion anisotropy. Phase diagrams in the
temperature-field plane for both easy-axis and easy-plane anisotropy of a
varying strength are constructed in the regimes of a moderate and strong DMI by
parallel tempering Monte Carlo simulations. For the considered range of
parameters the phase diagrams featuring up to four ordered phases are
identified. A skyrmion lattice (SkX) phase is found to be stabilized within
some temperature and field window for sufficiently large DMI and not too strong
anisotropy. For the systems with moderate (larger) DMI, a small easy-plane
(easy-axis) anisotropy is concluded to be beneficial by extending (shifting)
the field window of the SkX appearance to lower values. The Metropolis dynamics
is employed to probe the persistence of SkX upon quenching the field to zero or
small finite values. The most favorable conditions for the skyrmions
persistence are confirmed at low temperatures, small DMI and small easy-plane
anisotropy values.
