# Nonexistence and existence results for a 2$n$th-order $p$-Laplacian discrete Neumann boundary value problem

Document Type: Research Paper

Authors

1 Modern Business and Management‎ ‎Department‎, ‎Guangdong Construction Polytechnic‎, ‎Guangzhou 510440‎, ‎China.

2 Oriental Science and‎ ‎Technology College‎, ‎Hunan Agricultural University‎, ‎Changsha 410128‎, ‎China‎, ‎and Science College‎, ‎Hunan‎ ‎Agricultural University‎, ‎Changsha 410128‎, ‎China.

3 Packaging Engineering Institute‎, ‎Jinan University‎, ‎Zhuhai 519070‎, ‎China.

Abstract

This paper is concerned with a 2nth-order p-Laplacian difference equation. By using the
critical point method, we establish various sets of sufficient conditions for the nonexistence and existence of solutions for Neumann boundary value problem and give some new results. Results obtained successfully generalize and complement the existing ones.

Keywords

Main Subjects

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### History

• Receive Date: 15 November 2013
• Revise Date: 13 February 2015
• Accept Date: 24 September 2015