Nonexistence and Existence Results for a Fourth-Order p-Laplacian Discrete Neumann Boundary Value Problem

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• 作者：Xia Liu ; Yuanbiao Zhang ; Xiaoqing Deng
• 关键词：Nonexistence and existence ; Neumann boundary value problem ; p ; Laplacian ; Mountain Pass Lemma ; Discrete variational theory ; 39A10
• 刊名：Bulletin of the Malaysian Mathematical Sciences Society
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：39
• 期：1
• 页码：87-101
• 全文大小：489 KB
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• 作者单位：Xia Liu (1) (2)
  Yuanbiao Zhang (3)
  Xiaoqing Deng (4)
  
  1. Oriental Science and Technology College, Hunan Agricultural University, Changsha, 410128, China
  2. Science College, Hunan Agricultural University, Changsha, 410128, China
  3. Packaging Engineering Institute, Jinan University, Zhuhai, 519070, China
  4. School of Mathematics and Statistics, Hunan University of Commerce, Changsha, 410205, China
  
• 刊物类别：Mathematics, general; Applications of Mathematics;
• 刊物主题：Mathematics, general; Applications of Mathematics;
• 出版者：Springer Singapore
• ISSN：2180-4206

文摘

In this paper, a fourth-order nonlinear p-Laplacian difference equation is considered. Using the critical point theory, we establish various sets of sufficient conditions of the nonexistence and existence of solutions for Neumann boundary value problem and give some new results. The existing results are generalized and significantly complemented. Keywords Nonexistence and existence Neumann boundary value problem p-Laplacian Mountain Pass Lemma Discrete variational theory