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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

advances in mathematical physics

On the Existence of Central Configurations of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:mn>2</mml:mn><mml:mi>k</mml:mi><mml:mo>+</mml:mo><mml:mn>2</mml:mn><mml:mi>p</mml:mi><mml:mo>+</mml:mo><mml:mn>2</mml:mn><mml:mi>l</mml:mi></mml:mrow></mml:math>-Body Problems

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