Two positive solutions of a second order nonlinear difference equation involving the mean curvature operator

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Abstract

In this paper, we establish the existence of two positive solutions for a discrete mean curvature problem with Dirichlet boundary value conditions. The approach is based on a two-critical-point theorem. Our main result extends an existing conclusion in the literature. Moreover, three examples are presented to illustrate the validity and feasibility.

Keywords

difference equation / positive solution / two solutions / critical point theory / mean curvature operator / Dirichlet boundary value problem

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