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

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Abstract

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.

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Acknowledgments

This project is supported by Specialized Research Fund for the Doctoral Program of Higher Eduction of China (Grant No. 20114410110002), National Natural Science Foundation of China (Grant No. 11171078), Science and Research Program of Hunan Provincial Science and Technology Department (Grant No. 2012FJ4109) and Scientific Research Fund of Hunan Provincial Education Department (Grant No. 12C0170, 13C487).

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Authors and Affiliations

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

    Xia Liu

  2. Science College, Hunan Agricultural University, Changsha, 410128, China

    Xia Liu

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

    Yuanbiao Zhang

  4. School of Mathematics and Statistics, Hunan University of Commerce, Changsha, 410205, China

    Xiaoqing Deng

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  1. Xia Liu
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  2. Yuanbiao Zhang
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  3. Xiaoqing Deng
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Correspondence to Xiaoqing Deng.

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Communicated by Syakila Ahmad.

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Liu, X., Zhang, Y. & Deng, X. Nonexistence and Existence Results for a Fourth-Order p-Laplacian Discrete Neumann Boundary Value Problem. Bull. Malays. Math. Sci. Soc. 39, 87–101 (2016). https://doi.org/10.1007/s40840-015-0162-9

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  • DOI: https://doi.org/10.1007/s40840-015-0162-9

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