  We study the energetic and dynamic stability of coreless vortices in
nonrotated spin-1 Bose-Einstein condensates, trapped with a three-dimensional
optical potential and a Ioffe-Pritchard field. The stability of stationary
vortex states is investigated by solving the corresponding Bogoliubov
equations. We show that the quasiparticle excitations corresponding to
axisymmetric stationary states can be taken to be eigenstates of angular
momentum in the axial direction. Our results show that coreless vortex states
can occur as local or global minima of the condensate energy or become
energetically or dynamically unstable depending on the parameters of the
Ioffe-Pritchard field. The experimentally most relevant coreless vortex state
containing a doubly quantized vortex in one of the hyperfine spin components
turned out to have very non-trivial stability regions, and especially a
quasiperiodic dynamic instability region which corresponds to splitting of the
doubly quantized vortex.
