Geodesic
On the spectrum of the $p$-biharmonic operator involving $p$-Hardy's inequality
Abdelouahed El Khalil1 ; My Driss Morchid Alaoui2 ; Abdelfattah Touzani2
1Department of Mathematics and Statistics College of Science Al-Imam Mohammad Ibn Saud Islamic University (IMSIU) P.O. Box 90950 Riyadh 11623, Saudi Arabia
2Faculty 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
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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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