Multiplicity of solutions for discrete problems with double-well potentials

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 type critical points. In addition to simple discrete boundary-value problems, partial difference equations as 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