  An ubiquitous property of plasmas is the so-called Debye shielding of the
electrostatic potential. Important aspects of Debye screening concern, in
particular, the investigation of non-linear charge screening effects taking
place in strongly-coupled plasmas, that imply a reduction of the effective
charge characterizing the Debye-H\"{u}ckel potential. These effects are
particularly relevant in dusty plasmas which are characterized by high-Z
particles. The investigation of the effective interactions of these particles
has attracted interest in recent years especially for numerical simulations. In
this work we intend to analyze the consistency of the traditional mathematical
model for the Debye screening. In particular, we intend to prove that the 3D
Poisson equation involved in the DH model does not admit strong solutions. For
this purpose a modified model is proposed which takes into account the effect
of local plasma sheath (i.e., the local domain near test particles where the
plasma must be considered discrete). Basic consequences of the model are
discussed, which concern the asymptotic properties of the solutions determined
both for weakly and strongly coupled plasmas. As an application the charge
screening effect in strongly coupled plasmas is investigated and an explicit
expression of the effective charge for the asymptotic DH potential is
determined.
