2005-Oujda International Conference on Nonlinear Analysis, Oujda, Morocco.
Electron. J. Diff. Eqns., Conference 14 (2006), pp. 243-252.

Existence and uniqueness of a positive solution for a non homogeneous problem of fourth order with weights

Mohamed Talbi, Najib Tsouli

Abstract:
In this work we study the existence of a positive solutions to the non homogeneous equation
$$ \Delta( |\Delta u|^{p-2} \Delta u) = m |u|^{q-2}u $$
with Navier boundary conditions, where $1<p,q<p_2^*$ and $m\in L^\infty(\Omega)\setminus \{0\}$, $m\geq 0$. In the case $p>q$ and $m\in \mathcal{C}(\overline{\Omega})$, we prove the uniqueness of this solution.


Math Subject Classifications: 35J60, 35J30, 35J65.
Key Words: Ekeland's principle; p-biharmonic operator; Palais-Smale condition.

This article will be posted when the authors return the galley proofs

Mohamed Talbi
Département de Mathématiques et Informatique
Faculté des Sciences, Université Mohamed 1er
Oujda, Maroc
email: talbi_md@yahoo.fr
Najib Tsouli
University Mohamed 1er, Faculty of sciences
Department of Mathematics, Oujda, Morocco
e-mail: tsouli@sciences.univ-oujda.ac.ma

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