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On the $p$-biharmonic operator with critical Sobolev exponent

Volume 41 / 2014

Abdelouahed El Khalil, My Driss Morchid Alaoui, Abdelfattah Touzani Applicationes Mathematicae 41 (2014), 229-237 MSC: Primary 35G30; Secondary 35J50. DOI: 10.4064/am41-2-10

Abstract

We study the existence of solutions for a $p$-biharmonic problem with a critical Sobolev exponent and Navier boundary conditions, using variational arguments. We establish the existence of a precise interval of parameters for which our problem admits a nontrivial solution.

Authors

  • Abdelouahed El KhalilDepartment of Mathematics and Statistics
    College of Science
    Al-Imam Mohammad Ibn Saud
    Islamic University (IMSIU)
    P.O. Box 90950
    Riyadh 11623, Saudi Arabia
    e-mail
  • My Driss Morchid AlaouiFaculty of Sciences Dhar-Mahraz
    Department of Mathematics
    University Sidi Mohamed Ben Abdellah
    P.O. Box 1796 Atlas
    Fez 30000, Morocco
    e-mail
  • Abdelfattah TouzaniFaculty of Sciences Dhar-Mahraz
    Department of Mathematics
    University Sidi Mohamed Ben Abdellah
    P.O. Box 1796 Atlas
    Fez 30000, Morocco
    e-mail

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