  YES! We introduce a variable power Maxwell nonlinear electrodynamics theory
which can remove the singularity of electric field of point-like charges at
their locations. One of the main problems of Maxwell's electromagnetic field
theory is related to the existence of singularity for electric field of
point-like charges at their locations. In other words, the electric field of a
point-like charge diverges at the charge location which leads to an infinite
self-energy. In order to remove this singularity a few nonlinear
electrodynamics (NED) theories have been introduced. Born-Infeld (BI) NED
theory is one of the most famous of them. However the power Maxwell (PM) NED
cannot remove this singularity. In this paper, we show that the PM NED theory
can remove this singularity, when the power of PM NED is less than
$s<\frac{1}{2}$.
