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Research Article | Open Access

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

Liqun Jiang1,2( ), Lin Zou3, Xiaoyan Chen1
School of Mathematics, Changsha University, Changsha 410022, China
College of Mathematics and Statistics, Jishou University, Jishou 416000, China
Business school, Hunan University, Changsha 410082, China
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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 equationpositive solutiontwo solutionscritical point theorymean curvature operatorDirichlet boundary value problem

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Electronic Research Archive
Volume 33 Issue 6,
June 2025
Pages 3699-3715
DOI: 10.3934/era.2025164

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Cite this article:
Jiang L, Zou L, Chen X. Two positive solutions of a second order nonlinear difference equation involving the mean curvature operator. Electronic Research Archive, 2025, 33(6): 3699-3715. https://doi.org/10.3934/era.2025164

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Received: 31 December 2024
Revised: 06 May 2025
Accepted: 04 June 2025
Published: 12 June 2025
©2025 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)