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Oct 12, 2015 at 10:41 comment added Alexandre Eremenko @Suvrit: Interesting! Thanks for the reference.
Oct 12, 2015 at 1:53 comment added Suvrit I just saw this claim for a proof for the case $n=3$ with equal $a_j$: sciencedirect.com/science/article/pii/S0167278915001347
Jan 28, 2015 at 14:48 comment added Alexandre Eremenko I do not understand what is the relation between the problems. Can you explain? In Maxwell problem $x_j$ are FIXED.
Jan 28, 2015 at 4:55 comment added Richard Montgomery This is quite similar to the problem regarding finiteness of the number of central configurations for the n-body problem which made it into Smale's problem list, known for centuries for n=3, proven for n=4 [Moeckel and Hampton] and with substantial results for n=5 [Albouy and Kaloshin]. To get to Maxwell's from the n-body one, formally take n bodies and place them at the $x_j$, with masses $a_j$, and then add a n+1st body, at variable x, with mass $\epsilon$ and let $\epsilon \to 0$. Hmmm...
Dec 16, 2014 at 23:17 history edited Alexandre Eremenko CC BY-SA 3.0
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S Dec 16, 2014 at 23:02 history answered Alexandre Eremenko CC BY-SA 3.0
S Dec 16, 2014 at 23:02 history made wiki Post Made Community Wiki by Alexandre Eremenko