  We examine the multistability associated with miscibility-immiscibility
conditions for a two-component Bose-Einstein condensate coupled to the light
field in an optical cavity. For a strongly immiscible condition, the system
exhibits a variety of density structures, including separated state, stripe
state, and their coexistence. The multistability arises from these spatial
structures of the two-component condensate, which significantly alter the
hysteresis curve with respect to the intensity of cavity pumping. We present a
variational approach to confirm our numerical results.
