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Existence of Multiple Anti-Periodic Solutions for a Higher Order Nonlinear Difference Equation

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Abstract

By using the variational approach and critical point theory, we establish several criteria for the existence of at least three anti-periodic solutions for a higher order difference equation with p-Laplacian and which contains both advance and retardation. As special cases, we obtain results when the nonlinear function is free of advance or retardation. To illustrate our results, we discuss some consequences of our main results when the function is specified. Our work complements the existing results in the literature. Finally, we present an example to show the applicability of the results.

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Acknowledgements

Lingju Kong’s research was supported in part by the NNSF of China (No. 11671406) and by a University of Tennessee at Chattanooga SimCenter–Center of Excellence in Applied Computational Science and Engineering (CEACSE) grant.

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Authors and Affiliations

  1. Department of Mathematics, University of Connecticut, Storrs, CT, 06269, USA

    Sougata Dhar

  2. Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, TN, 37403, USA

    Lingju Kong

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  1. Sougata Dhar
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  2. Lingju Kong
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Correspondence to Sougata Dhar.

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Dhar, S., Kong, L. Existence of Multiple Anti-Periodic Solutions for a Higher Order Nonlinear Difference Equation. Mediterr. J. Math. 18, 23 (2021). https://doi.org/10.1007/s00009-020-01689-y

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  • DOI: https://doi.org/10.1007/s00009-020-01689-y

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