  We consider the non-linear classical field theory which results from adding
to the Maxwell's Lagrangian the contributions from the weak-field
Euler-Heisenberg Lagrangian and a non-uniform part which involves derivatives
of the electric and magnetic fields. We focus on the electrostatic case where
the magnetic field is set to zero, and we derive the modified Gauss law,
resulting in a higher order differential equation. This equation gives the
electric field produced by stationary charges in the higher order non-linear
electrodynamics. Specializing for the case of a point charge, we investigate
the solutions of the modified Gauss law and calculate the correction to the
Coulomb law.
