On the spectrum of the p-biharmonic operator involving p-Hardy's inequality

Abdelouahed El Khalil; My Driss Morchid Alaoui; Abdelfattah Touzani

Abdelouahed El Khalil ; My Driss Morchid Alaoui ; Abdelfattah Touzani

Applicationes Mathematicae, Tome 41 (2014), p. 239-246 / Harvested from The Polish Digital Mathematics Library

Résumé

In this paper, we study the spectrum for the following eigenvalue problem with the p-biharmonic operator involving the Hardy term: ${Δ (| Δ u |}^{p - 2} {Δ u) = λ (| u |}^{p - 2} u) / (δ {(x)}^{2 p})$ in Ω, $u \in W ₀^{2, p} (Ω)$ . 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.

Publié le : 2014-01-01

Zbl 1304.35466

EUDML-ID : urn:eudml:doc:280054

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     title = {On the spectrum of the p-biharmonic operator involving p-Hardy's inequality},
     journal = {Applicationes Mathematicae},
     volume = {41},
     year = {2014},
     pages = {239-246},
     zbl = {1304.35466},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am41-2-11}
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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) pp. 239-246. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am41-2-11/