This article presents some multiplicity results for a general class of nonlinear discrete problems with double-well potentials.Variational techniques are used to obtain the existence of saddle-point Sports type critical points.In addition to simple discrete boundary-value problems, partial difference equations as Dabber well as problems involving discrete $p$-Laplacian are considered.
Also the boundedness of solutions is studied and possible applications, e.g.in image processing, are discussed.