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On a critical fourth order Leray–Lions \(p(\cdot )\)-Kirchhoff type problem with no-flux boundary condition

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Abstract

Using variational methods combined with the genus theory, we investigate in this paper, the existence of nontrivial weak solutions for a class of fourth order critical \(p(\cdot )\)-Kirchhoff type problem involving the Leray–Lions type operators with indefinite weight and no flux boundary condition. Accurately, we show the existence of at least k pairs of nontrivial weak solutions for the given problem.

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Acknowledgements

Our sincere gratitude goes to the editor and the anonymous referees for their valuable suggestions which contributed significantly to improving the quality of this article

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Sciences, University Mohammed I, Oujda, Morocco

    Khalid Soualhine, Mohammed Filali & Najib Tsouli

  2. CRMEF, Oujda, Morocco

    Mohamed Talbi

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  1. Khalid Soualhine
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  3. Mohammed Filali
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Correspondence to Khalid Soualhine.

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Soualhine, K., Talbi, M., Filali, M. et al. On a critical fourth order Leray–Lions \(p(\cdot )\)-Kirchhoff type problem with no-flux boundary condition. São Paulo J. Math. Sci. 18, 277–299 (2024). https://doi.org/10.1007/s40863-024-00403-0

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