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The third order spectrum of the $p$-biharmonic operator with weight

Volume 41 / 2014

Khalil Ben Haddouch, Najib Tsouli, Zakaria El Allali Applicationes Mathematicae 41 (2014), 247-255 MSC: 35P30, 35J40. DOI: 10.4064/am41-2-12

Abstract

We show that the spectrum of $\varDelta ^{2}_{p} u + 2\beta \cdot \nabla (|\varDelta u|^{p-2}\varDelta u) + |\beta |^{2}|\varDelta u|^{p-2}\varDelta u=\alpha m|u|^{p-2}u$, where $\beta \in \mathbb {R}^{N}$, under Navier boundary conditions, contains at least one sequence of eigensurfaces.

Authors

  • Khalil Ben HaddouchDepartment of Mathematics
    University Mohamed I
    Oujda, Morocco
    e-mail
  • Najib TsouliDepartment of Mathematics
    University Mohamed I
    Oujda, Morocco
    e-mail
  • Zakaria El AllaliDepartment of Mathematics
    University Mohamed I
    Oujda, Multidisciplinary Faculty of Nador, Morocco
    e-mail

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