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Three solutions to a Neumann boundary value problem driven by p(x)-biharmonic operator

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Abstract

In this article, we establish the existence of at least three distinct weak solutions for a specific class of quasilinear elliptic equations. These equations incorporate the p(x)-biharmonic operator and are constrained by Neumann boundary conditions. Our technical approach is primarily founded on Ricceri’s three critical points theorem (Nonlinear Anal 70:3084–3089, 2009). In addition, we give an example to show our key findings.

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Funding

M.K. Hamdani was supported by the Tunisian Military Research Center for Scienceand Technology Laboratory LR19DN01. M.K. Hamdani expresses his deepest gratitude to the Mil-itary Aeronautical Specialities School, Sfax (ESA) for providing an excellent atmosphere for work.

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Authors and Affiliations

  1. Team of Modeling and Scientific Computing, LaMAO, Multidisciplinary Faculty of Nador, Mohammed First University, Oujda, Morocco

    Zakaria El Allali

  2. Science and Technology for Defense Laboratory LR19DN01, Center for Military Research, Military Academy, Grombalia, Tunisia

    Mohamed Karim Hamdani

  3. Military School of Aeronautical Specialities, Sfax, Tunisia

    Mohamed Karim Hamdani

  4. Mathematics Department, Faculty of Science of Sfax, University of Sfax, Sfax, Tunisia

    Mohamed Karim Hamdani

  5. LISTI, National School of Applied Sciences of Agadir, Ibn Zohr University, Agadir, Morocco

    Said Taarabti

Authors
  1. Zakaria El Allali
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  2. Mohamed Karim Hamdani
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  3. Said Taarabti
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All authors read and approved the final manuscript and all authors have agreed to the authorship and the order of authorship for this manuscript. All authors have the appropriate permissions and rights to the reported data.

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Correspondence to Mohamed Karim Hamdani.

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Allali, Z.E., Hamdani, M.K. & Taarabti, S. Three solutions to a Neumann boundary value problem driven by p(x)-biharmonic operator. J Elliptic Parabol Equ (2024). https://doi.org/10.1007/s41808-023-00257-1

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