MULTIPLICITY OF SOLUTIONS FOR DISCRETE PROBLEMS WITH DOUBLE-WELL POTENTIALS

作者：Otta Josef^*; Stehlik Petr

来源：Electronic Journal of Differential Equations, 2013, 186.

• Discrete problem
• boundary value problem
• p-Laplacian
• partial difference equation
• bistable equation
• double-well
• saddle-point
• variational method
• periodic problem
• Neumann boundary condition

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.

• 出版日期2013-8-23