Geodesic
On the spectrum of the $p$-biharmonic operator involving $p$-Hardy's inequality
Abdelouahed El Khalil1 ; My Driss Morchid Alaoui2 ; Abdelfattah Touzani2
1 Department of Mathematics and Statistics College of Science Al-Imam Mohammad Ibn Saud Islamic University (IMSIU) P.O. Box 90950 Riyadh 11623, Saudi Arabia
2 Faculty of Sciences Dhar-Mahraz Department of Mathematics University Sidi Mohamed Ben Abdellah P.O. Box 1796 Atlas Fez 30000, Morocco
Applicationes Mathematicae, Tome 41 (2014) no. 2-3, pp. 239-246

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

In this paper, we study the spectrum for the following eigenvalue problem with the $p$-biharmonic operator involving the Hardy term: $$\varDelta (|\varDelta u|^{p-2}\varDelta u)= \lambda \frac {|u|^{p-2}u}{\delta (x)^{2p}} \hbox { in } \varOmega , \ u\in W_0^{2,p}(\varOmega ).$$ By using the variational technique and the Hardy–Rellich inequality, we prove that the above problem has at least one increasing sequence of positive eigenvalues.
DOI : 10.4064/am41-2-11
Keywords: paper study spectrum following eigenvalue problem p biharmonic operator involving hardy term vardelta vardelta p vardelta lambda frac p delta hbox varomega varomega using variational technique hardy rellich inequality prove above problem has least increasing sequence positive eigenvalues

Abdelouahed El Khalil 1 ; My Driss Morchid Alaoui 2 ; Abdelfattah Touzani 2

1 Department of Mathematics and Statistics College of Science Al-Imam Mohammad Ibn Saud Islamic University (IMSIU) P.O. Box 90950 Riyadh 11623, Saudi Arabia
2 Faculty of Sciences Dhar-Mahraz Department of Mathematics University Sidi Mohamed Ben Abdellah P.O. Box 1796 Atlas Fez 30000, Morocco 
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Abdelouahed El Khalil; My Driss Morchid Alaoui; Abdelfattah Touzani. On the spectrum of the $p$-biharmonic operator involving $p$-Hardy's inequality. Applicationes Mathematicae, Tome 41 (2014) no. 2-3, pp. 239-246. doi: 10.4064/am41-2-11

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