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The existence and uniqueness of equilibrium points, including Lagrange Pointsand Jiang-Yeh Points, of a galactic system with supermassive binary black holesembedded in a centrally cuspy galactic halo are investigated herein. Differingfrom the previous results of non-cuspy galactic profiles that Jiang-Yeh Pointsonly exist under a particular condition, it is found here that the LagrangePoints, L2, L3, L4 and L5, Jiang-Yeh Points, JY1 and JY2, exist under generalconditions. The stability analysis shows that L2, L3, JY1 and JY2 are unstable.However, L4 and L5 are only unstable when the galactic total mass is smallerthan a critical mass; otherwise they become neutrally stable centers. Theseresults will be important for further studies on the cores of early-typegalaxies.

Galaxies with Supermassive Binary Black Holes: (II) A Model with Cuspy Galactic Density Profiles