Opuscula Math. 34, no. 4 (2014), 683-690
http://dx.doi.org/10.7494/OpMath.2014.34.4.683

Opuscula Mathematica

# Constant-sign solutions for a nonlinear Neumann problem involving the discrete p-Laplacian

Pasquale Candito
Giuseppina D'Aguí

Abstract. In this paper, we investigate the existence of constant-sign solutions for a nonlinear Neumann boundary value problem involving the discrete $$p$$-Laplacian. Our approach is based on an abstract local minimum theorem and truncation techniques.

Keywords: constant-sign solution, difference equations, Neumann problem.

Mathematics Subject Classification: 39A10, 39A12, 34B15.

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• Pasquale Candito
• University of Reggio Calabria, Department DICEAM, Via Graziella (Feo Di Vito), 89122 Reggio Calabria, Italy
• Giuseppina D'Aguí
• University of Messina, Department of Civil, Computer, Construction, Environmental Engineering and Applied Mathematics, 98166 - Messina, Italy
• Revised: 2014-07-15.
• Accepted: 2014-07-25.