Answer to Earnshaw's theorem says that no particle can be in stable equilibrium under the action of electrostatic forces alone.,........

As Feynman says, it requires E=0E=0 eventually (P0)(P0) and all EE vectors looking inwards (like neighborhood minima) around that point. At that point how about we utilize Gauss' law: figure flux. It will be not zero, which implies that such point does not exist. 

What is feasible is a round shell with some charge and same sign charge in its center. You encase your focused accuse of surface. Presently there is field from the shell and from the charge crossing it. Bo-ya, this field has non-zero flux through the surface.