  Critical curves "critical current - external magnetic field" of long
Josephson junctions with inhomogeneity and variable width are studied. We
demonstrate the existence of the regions of magnetic field where some fluxon
states are stable only, if the external current through the junction is
different from zero. Position and size of such regions depend on length of the
junction, its geometry, parameters of inhomogeneity and form of the junction.
The noncentral (left and right) pure fluxon states are appeared in the
inhomogeneous Josephson junction with increase in the junction length. We
demonstrate new bifurcation points with change in width of the inhomogeneity
and amplitude of the Josephson current through the inhomogeneity.
