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Sign-Changing Solutions for Discrete Second-Order Periodic Boundary Value Problems

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Abstract

In this paper, we study the existence of sign-changing solutions and positive solutions for second-order nonlinear difference equations on a finite discrete segment with periodic boundary condition provided that the nonlinearity is asymptotically linear at infinity. The critical point theory and variational methods are employed to discuss this problem.

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Acknowledgments

The authors thank the anonymous referee very much for the careful reading the manuscript and for the valuable suggestions and comments. Tieshan He thanks School of Mathematics and Computational Science of Sun Yat–Sen University for the hospitality when he was visiting there in 2011.

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Authors and Affiliations

  1. School of Computation Science, Zhongkai University of Agriculture and Engineering, Guangzhou, 510225, Guangdong, People’s Republic of China

    Tieshan He & Chuanyong Chen

  2. School of Mathematics and Computational Science, Xiangtan University, Xiangtan, 411105, Hunan, People’s Republic of China

    Yiwen Zhou

  3. School of Mathematics and Computational Science, Sun Yat-Sen University, Guangzhou, 510275, Guangdong, People’s Republic of China

    Yuantong Xu

Authors
  1. Tieshan He
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  2. Yiwen Zhou
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  3. Yuantong Xu
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  4. Chuanyong Chen
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Corresponding author

Correspondence to Chuanyong Chen.

Additional information

Communicated by Syakila Ahmad.

Supported by the NNSF of China (No. 11201504) and the Scientific Research Plan Item of Guangdong Provincial Department of Education (No. 2011TJK468).

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He, T., Zhou, Y., Xu, Y. et al. Sign-Changing Solutions for Discrete Second-Order Periodic Boundary Value Problems. Bull. Malays. Math. Sci. Soc. 38, 181–195 (2015). https://doi.org/10.1007/s40840-014-0012-1

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  • DOI: https://doi.org/10.1007/s40840-014-0012-1

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