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A nonlinear boundary problem involving the p -bilaplacian operator

Author

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  • Abdelouahed El Khalil
  • Siham Kellati
  • Abdelfattah Touzani

Abstract

We show some new Sobolev's trace embedding that we apply to prove that the fourth-order nonlinear boundary conditions Δ p 2 u + | u | p − 2 u = 0 in Ω and − ( ∂ / ∂ n ) ( | Δ u | p − 2 Δ u ) = λ Ï | u | p − 2 u on ∂ Ω possess at least one nondecreasing sequence of positive eigenvalues.

Suggested Citation

  • Abdelouahed El Khalil & Siham Kellati & Abdelfattah Touzani, 2005. "A nonlinear boundary problem involving the p -bilaplacian operator," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2005, pages 1-13, January.
    • Handle: RePEc:hin:jijmms:969812
    DOI: 10.1155/IJMMS.2005.1525
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    Cited by:

    1. Abdelouahed El Khalil & My Driss Morchid Alaoui & Abdelfattah Touzani, 2014. "On the -Biharmonic Operator with Critical Sobolev Exponent and Nonlinear Steklov Boundary Condition," International Journal of Analysis, Hindawi, vol. 2014, pages 1-8, March.

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