  Numerical results are presented for the spin excitations of a two-dimensional
electron gas confined to a quantum well of width w. Spin waves and charged
skyrmion excitations are studied for filling factors nu=1, 3, and 1/3. Phase
diagrams for the occurrence of skyrmions of different size as a function of w
and the Zeeman energy are calculated. For nu=3, skyrmions occur only if w is
larger than about twice the magnetic length. A general necessary condition on
the interaction pseudopotential for the occurrence of stable skyrmion states is
proposed.
