3 problems

One-dimensional Maxwell bound. For any values of the charges, the function $V_{\alpha}^*(x)$ has at most $2l-1$ real critical points. This is a stronger one-dimensional version of…

Let $V_{\alpha}(\bar x)$ be the potential of a generic configuration of point charges of the same sign, and let $a_{\alpha}^j$ denote the number of its critical points of index $j$…

Conjecture 1.3 (Maxwell; [11], see also Section 4). The total number of points of equilibrium, all assumed nondegenerate, of any configuration with $l$ charges in $\mathbb{R}^{3}$…