Electronic Journal of Differential Equations,
Vol. 2013 (2013), No. 186, pp. 1-14.

Title: Multiplicity of solutions for discrete problems with double-well potentials

Authors: Josef Otta   (Univ. of West Bohemia, Pilsen, Czech Republic)
         Petr Stehlik (Univ. of West Bohemia, Pilsen, Czech Republic)

Abstract:
 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.

Submitted April 29, 2013. Published August 23, 2013.
Math Subject Classifications: 39A12, 34B15.
Key Words: Discrete problem; boundary value problem; p-Laplacian;
           partial difference equation;  bistable equation; 
           double-well; saddle-point; variational method; 
           periodic problem; Neumann boundary condition.