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

Liqun Jiang; Lin Zou; Xiaoyan Chen; Liqun Jiang; Lin Zou; Xiaoyan Chen

doi:10.3934/era.2025164

Electronic Research Archive

2025, Volume 33, Issue 6: 3699-3715. doi: 10.3934/era.2025164

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Research article

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

1.
School of Mathematics, Changsha University, Changsha 410022, China
2.
College of Mathematics and Statistics, Jishou University, Jishou 416000, China
3.
Business school, Hunan University, Changsha 410082, China

Received: 31 December 2024 Revised: 06 May 2025 Accepted: 04 June 2025 Published: 12 June 2025

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.
- difference equation,
- positive solution,
- two solutions,
- critical point theory,
- mean curvature operator,
- Dirichlet boundary value problem
Citation: Liqun Jiang, Lin Zou, Xiaoyan Chen. Two positive solutions of a second order nonlinear difference equation involving the mean curvature operator[J]. Electronic Research Archive, 2025, 33(6): 3699-3715. doi: 10.3934/era.2025164

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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.

References

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