On the Existence of Central Configurations of2k+2p+2l-Body Problems

We prove the existence of central configurations of the 2k+2p+2l-body problems with Newtonian potentials in R3. In such configuration, 2k masses are symmetrically located on the z-axis, 2p masses are symmetrically located on the y-axis, and 2l masses are symmetrically located on the x-axis, respectively; the masses symmetrically about the origin are equal