Electron. J. Diff. Equ., Vol. 2013 (2013), No. 186, pp. 1-14.

Multiplicity of solutions for discrete problems with double-well potentials

Josef Otta, Petr Stehlik

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.

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Josef Otta
University of West Bohemia in Pilsen
Univerzitni 22, 312 00 Czech Republic
email: josef.otta@gmail.com
Petr Stehlík
University of West Bohemia in Pilsen
Univerzitni 22, 312 00 Czech Republic
email: pstehlik@kma.zcu.cz

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