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Homoclinic Solutions for Partial Difference Equations with Mixed Nonlinearities

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Abstract

In this paper, we consider a class of partial difference equations with sign-changing mixed nonlinearities and unbounded potentials. Some sufficient conditions for the existence and multiplicity of homoclinic solutions are obtained by using critical point theory. Even for ordinary difference equations, our results significantly improve some existing ones.

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Acknowledgements

We would like to take this opportunity to thank the reviewers for their constructive and helpful comments and suggestions. This work is supported by the National Natural Science Foundation of China (Grant Nos. 11971126, 12201141) and the Program for Changjiang Scholars and Innovative Research Team in University (Grant No. IRT\(_{-}\)16R16).

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Authors and Affiliations

  1. School of Mathematics and Information Science, Guangzhou University, Guangzhou, 510006, China

    Peng Mei & Zhan Zhou

  2. Guangzhou Center for Applied Mathematics, Guangzhou University, Guangzhou, 510006, China

    Peng Mei & Zhan Zhou

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  1. Peng Mei
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  2. Zhan Zhou
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Correspondence to Zhan Zhou.

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Mei, P., Zhou, Z. Homoclinic Solutions for Partial Difference Equations with Mixed Nonlinearities. J Geom Anal 33, 117 (2023). https://doi.org/10.1007/s12220-022-01166-w

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