  We discuss the stability of the Skyrmion solution in the presence of a finite
isospin chemical potential $\mu$. Solving numerically the mass of the Skyrmion
as function of $\mu$, we find a critical value $\mu_c=222.8$ MeV where the
Skyrmion mass vanishes. We compare the exact numerical treatment with an
analytical discussion based on a special shape for the profile of the Skyrmion
due to Atiyah and Manton. The extension of this ansatz for finite $\mu$ works
quite well for $\mu<121$ MeV. Then, for small values of $\mu$, where the
analytical approach is valid, we consider the possibility of having an angular
deformation for the Skyrmionic profile, which is possible for finite values of
$\mu$. This is however, a small effect. Finally we introduce finite temperature
corrections, which strength the instability induced by the chemical potential,
finding the dependence of the critical temperature on $\mu$.
