  We study effects of a potential barrier on collective modes of superfluid
Bose gases in optical lattices. We assume that the barrier is created by local
suppression of the hopping amplitude. When the system is in a close vicinity of
the Mott transition at commensurate fillings, where an approximate
particle-hole symmetry emerges, there exist bound states of Higgs amplitude
mode that are localized around the barrier. By applying the Gutzwiller
mean-field approximation to the Bose-Hubbard model, we analyze properties of
normal modes of the system with a special focus on the Higgs bound states. We
show that when the system becomes away from the Mott transition point, the
Higgs bound states turn into quasi-bound states due to inevitable breaking of
the particle-hole symmetry. We use a stabilization method to compute the
resonance energy and line width of the quasi-bound states. We compare the
results obtained by the Gutzwiller approach with those by the Ginzburg-Landau
theory. We find that the Higgs bound states survive even in a parameter region
far from the Mott transition, where the Ginzburg-Landau theory fails.
